There’s nothing wrong with waiting if you have any doubts. You risk nothing.
However, you may drive yourself nuts obsessing and worrying about where you’re going to college when you already have a pretty good option in front of you. You could simply commit to Princeton and move on with your life. And have some fun with your senior year.
In my opinion, trying to research whether attending Harvard, Yale, MIT or Princeton will give you the best chance at getting into a top MBA program is a good way to ruin the rest of your senior year. You really won’t be able to find out the answer to this question, because the full information isn’t fully released. Even if you discover that an MBA program accepts 11% of Yale grads and 8% of Princeton grads, you will have no idea whether the caliber of those Princeton and those Yale grads was the same - the schools won’t let you review their applications, and unless you can, the admission percentage data is meaningless. Bear in mind that these applicants all worked at jobs before applying to business school, and the jobs and their job performance also figured prominently in the admissions criteria.
Another caveat: you have career goals and probable majors selected. A college admissions officer told me that 70% of college students nationally change their majors. Another at a top 25 school told me that they pay no attention to the major chosen, because the students so often change majors. Many students have their career picked out in their senior year in high school. You’ll find that most will not be in that previously chosen career ten years later (and many will have already changed careers at least once, five years after college graduation).
I started out writing magazine articles after college, was quite successful, wrote for numerous prominent magazines back when there were magazines, decided I hated it after a couple years, and quit. A couple careers later, I’m a business consultant. No one would have believed that the guy who, seated at the head table at a banquet filled with writers and photographers, wore a 3-piece suit and no shirt (yes, he was being a clown) would be a Congressman today, even him.
I would recommend that you not choose the college based on which one will give you the best chance at getting into an M7 business school. All of the four schools on your list will give you a chance at getting into one of these, and the one that will will most likely be the one that you fit into the best.
If you want to consider other schools, try to figure out which one you’ll like to attend the best. For visits, this is up to you and your financial resources, but I wouldn’t spend any money investigating those other schools until you’ve been accepted, because any or all could accept you or reject you.
Best of luck - it’s nice to know that you have one school under your belt that has accepted you and given you a solid financial aid offer.