Interesting comments about Harvard being seen as stronger world wide. That seems to contradict this:
https://www.timeshighereducation.com/world-university-rankings/2018/world-ranking#!/page/0/length/25/sort_by/rank/sort_order/asc/cols/stats
Rankings and prestige are two different things. USWR’s undergrad national ranking has Harvard second to Princeton but you will not find anyone arguing that Princeton enjoys greater global prestige over Harvard.
It’s an odd question. If you think you’re qualified to master Stanford academics, you should know it and HYP are all in the top academic tier. The end.
Unles you plan to be a pro athlete and want to know which will serve you better in that respect. Then, there’s a different answer. Or if all that matters to you is who thinks more of which in some foreign country. (Even so, the smart folks will know the top tier, not mince between S and HYP.)
But I will say, S is no easy row to hoe.
Well yes getting a full scholarship at Stanford will definitely be a strong plus point and I know at HYP I would have to apply for means based which will still be I believe be significant assistance but nowhere near 100%. But my parents have said they don’t want that to be the main reason for my decision. My sport is tennis and I think the men’s practice commitment is 3 hours every day, as well as traveling to matches and tournaments. That would be the same at HYP although Ivy tennis is not so intensive and maybe in CA there is more traveling too.
I guess that’s why they say that being an athlete at Stanford is the hardest place of all because both the athletics and the academics are so high level !
I wouldn’t base my college decision on similarities to a fictional Harry Potter-like building. Stanford’s campus is extremely large, one of the largest in the country, and extremely beautiful in its own respect. And no I’m not an alum, but I do live in the vicinity, so I’m biased that way.
Stanford does fine in global prestige. . For example, in the most QS world reputation subscores at https://www.topuniversities.com/university-rankings/world-university-rankings/2018 . Harvard, Stanford, and MIT all tied with the best possible score for both global academic reputation and global employer reputation. In contrast, Yale did not make the top 10 in employer reputation. Princeton did not make top 30.
However, what surveyed employers in different countries think about the college is probably not relevant to the OP. Differences might be more relevant for specific career paths and/or locations. For example, if you want to work in investment banking on Wall Street; HYP would likely present more special opportunities and connections than S. And if you want to work at a tech company in Silicon Valley, S would likely present more special opportunities and connections than HYP.
There are also differences among specific majors. As touched on, Stanford has the edge over HY in engineering and CS… CS is is by far Stanford’s most popular major. . It also offers various unique interdisciplinary majors than tend to be popular with athletes, such as STS and Hum Bio. HY probably have the edge in economics, which is the most popular major at HY, as well as certain other fields…
The sports themselves no doubt have key differences, which ti sounds like the OP is more familiar with than I am. I’d expect you are generally competing at a higher level at Stanford and can more test how far you can go. However, you are probably more likely to be a key player at HYP, may be more likely to be among the competing lineup as a freshmen. It was my experience as an athlete at Stanford that Stanford practices are near the NCAA limit of 20 hours per week. Both professors and the administration appeared to make allowances to support athlete schedules and other unique athlete issues. I’m not sure how HYP compares.
@circuitrider but they will make you hungry for Taco Bell.
@dannythomas if you’re using tennis as a way to gain admission to top tier schools then base your decision more heavily on the major you plan to study. If HYP is better for your major and you like the course offerings and potential cohort then I’d recommend Ivy. Would your tennis experience be the same or better at HYP vs Stanford? If you get injured and can’t play tennis or tennis isn’t enjoyable for you anymore and you want to quit, your sport won’t affect your HYP aid package but it would affect Stanford’s. Just some things to think about. Lastly, envision yourself with the Stanford vs the HYP tennis teams. Which one can you see yourself getting along better with and hanging out with? Those bus rides are long 
Your choice of schools are great. I’d give the nudge to:
-HYP as far as status (imo)
-Stanford for weather
-??? for Tennis prestige (idk if this matters to you who has a better Conference reputation)
-??? for major (that’s on you to research)
-Harvard for the town Cambridge (great college town!) idk about YP
- Any one of the schools for job and career assistance (although the Harvard name is bar none the best, imo)
-If you like a smaller student body size, then really consider HYP as the campus would have a more intimate feel vs Stanford’s sprawling campus at 16k students (combined).
Good luck!
Are you sure that you would get a full scholarship for men’s tennis at Stamford? Men’s tennis is not a headcount sport. They only have the equivalent of 4.5 scholarships to fund the whole team.
It’s a good sponsorship package. My dad has been dealing with that side but you may be right , it may not be as much as 100% .
Some other points people have raised. Yes, the level of tennis at Stanford is far higher than any of the Ivy schools. Columbia in fact is the only Ivy to get close. There are several examples of pro players who went to Stanford or similar strong tennis schools and played successful pro tennis after graduating. From the Ivies I can only think of 1 ( Harvard ) and he halted his degree after a year to play professionally. But I’m also not banking on a pro career or I wouldn’t be going to college at all !
For my major I think political science is the most likely. Is there any advantage in doing that in any of those schools in particular?
I’m not worried about fighting for a spot on whatever team even though I know Stanford will be tougher. I want to play in the NCAA finals and usually only 1 Ivy school makes it there.
But I also like the idea of going to a school with a worldwide reputation since tennis isn’t e erything !
These schools are all known worldwide.
But you should not base your decision on prestige among relative peers, and even if you weren’t considering peers, prestige should still only be a minor consideration.
Instead, figure out some things that are important to you.and rank them, and other schools, according to those preferences.
For instance:
Academics
- Class sizes
- Majors and courses offered
- Academic vibe (intellectual vs. pre-professional)
- Curriculum (required courses? distribution requirements?)
- Ease of changing your major (so many kids do, or want to)
Environment:
- Location
- Setting (urban/rural/suburban)
- Weather
- Campus look/convenience
Social vibe:
- Sports scene (of particular interest to you, probably)
- Party/Greek scene
- Clubs
- Things to so off-campus
- Dorms/food
And, obviously, cost. Be sure to include travel cost.
If you choose your apps and final decision based on these things – and visit if you are torn – you will only have good options when acceptances roll in.
For what it’s worth, here are some ways these schools compare to each other:
- Harvard is in Boston and has the highest percentage of grad students. Harvard has a long history of producing leaders. No top school in the US has been doing it longer. Harvard is JFK.
- Stanford is known for its sporty and techy vibes, and for good reason. They rival Harvard for overall graduate program quality, which is saying something. Stanford's campus is different architecturally. Stanford is Steve Jobs.
- Yale is the diva of this quartet, the most humanities-rich among them -- and it is (thus) the least STEMy, though there is quality there. Yale has residential colleges and New Haven is known for its pizza. Yale is Meryl Streep.
- Princeton is the most undergraduate-focused of these four schools. Students interact a lot with their profs, a senior thesis is required, and the social scene is known for eating clubs. Princeton is Einstein.
Just be careful and don’t count your chickens too fast. Until you have a letter in hand, you have nothing. The coaches will promise the world. They have limited pull in admissions. This isn’t football at Alabama (or even Stanford). If you are not projected to be the #1 or #2 your likely amount will be way less than 100%. It may not even be 100% at #1. Another tennis player that I think was going to be #1 at Duke got 70%. At HPY they may not even be able to get you past admissions. Don’t stop looking other places until you have a letter in your hand.
I’ve long considered Stanford to be at least the equivalent of HYP in all areas except snootiness.
However, a very nice book originated from a Harvard alumnus, The Inner Game of Tennis.
It seems to me if the OP is looking for two things beyond athletics----the best option for “political science” and the greatest “worldwide prestige”, it would be nice to get an offer from Harvard to compare.
But if you’re a fan of Taco Bell…
Omgeee the reference to Taco Bell and Stanford!!! I’ve never been to the campus but that would make me hungry! It’s a poor substitute for the real thing (Alberto’s, Roberto’s, Lolita’s…etc.) but I still eat it once in a while 
To get back to OP topic, if you don’t think tennis is an option post grad, then use the sport as a means to get the best education for your major. Consider where you want to work and how the reputation of the school and major will affect that. You should love the school and environment too, so visiting is important. The overnights will give you good insight to team chemistry. My son had Harvard as an option but he found the atmosphere too, shall we say, social status oriented for his liking. He’s a casual sporty So Cal guy and he’s so not into that (the clubs and such).
You can’t go wrong with any of those schools; they are all excellent and you can get a superb education at any one of them. @prezbucky laid out some important criteria to consider when comparing the schools. Spend some time visiting the campuses, sit in on classes, spend time with team members, and go with your gut (and pocketbook)!
With any potential college choice, make sure you would feel comfortable during your time there. As in the case below, an unsuitable decision can work as a source of regret:
Are you being actively recruited by HYP? If not, your chances would be the same as any applicant with similar qualifications. If you are, then plenty of good advice upthread on what you should be considering. If not, take your bird in hand with Stanford. Financially, you might be better off at HYP than Stanford even with an athletic scholarship. Your dad needs to work with the Stanford coach on what your net price will be after the athletic scholarship and need based aid. He can run the NPC for HYP to get an idea of net price there. Your athletic scholarship is subject to loss if you choose or cannot play, but Stanford need based aid could kick in to make up for it.