I am choosing colleges to apply to next year, and my top four are currently Princeton, Duke, MIT, and Penn. My go-to majors are engineering and physics, but I also have interests in economics and political science that I may wish to pursue in college. Which of the colleges I listed, or colleges similar to them, is the best for undecided students with a wider range of interests?
For flexibility. I suggest hot yoga. 
For school choices you need to be admitted for them to have any options for you at all.
I’m not kidding now. At this moment you should be getting your Princeton review. Forbes USNWR and start a big list of reaches (which are all of those listed even if you are a likely noble prize winner) and about 20 to 30 more. Matches which based on generic stats say you are in the range but still can be a 50 50 proposition based on quality of essays ecs recommendations and college needs in that moment. Finally safeties. Public schools in your state that meet your stats. Schools with auto admits with certain scores and algorithmic admissions.
You then winnow the list by your perceived tastes and preferences.
Then and most important you must make sure you can afford these school realistically if you get in. And if it’s the no merit aid category like you listed and your not going to get a lot of FA you must be honest. There are so many threads on here of heartbroken seniors who can’t understand why Vanderbilt is too expensive and now I have to go to x. As an example.
Once you have the three categories. The affordability and the preferences lined up to a manageable number. Then you can dive into these schools statistics policies and procedures And threads here are helpful when you can keyword switching majors at Georgetown and see what comes up
Good luck. It’s a thrilling ride!
I would say MIT, my cousin went in as an engineering and physics major and then he later switched to economics and is now doing amazing at a huge company. Definitely MIT and make sure to ED there cause that is really important
^ MIT doesn’t do ED.
Start with matches and safeties. Worry about reaches later.