I see several people telling you to definitely choose a first rank university. I'm not sure I agree.

Here's my experience. I applied to just MIT and my state university (University of Washington). I got on MIT's waiting list but was ultimately not accepted, so went to UW. I would certainly have gone to MIT had I been accepted, but my thinking now is that if I did that, I would not have had enough free time in college to write Crypto++ and think about anonymous protocols, Tegmark's multiverse, anthropic reasoning, etc., and these spare-time efforts have probably done more for my "career" than the MIT name or what I might have learned there.

So if you are someone who can use free time productively, you might want to consider going to a college where you don't have to spend too much effort on your classes, where, face it, a lot of the stuff you learn will ultimately turn out to be not very useful for what you end up doing.

There is a huge amount of uncertainty here. There is no perfect strategy - I think you have to just rank schools as best you can by your own preferences and then go to the top one you get into by some semi-arbitrary date.

That said once at college there are a variety of things that make a huge difference. Read important textbooks more than is strictly required. Experiment with learning strategies - study in groups or alone, taking notes, making flashcards. Read journals every once in a while to check your progress. Go to department seminars once you you feel comfortable. Play with math (or computers, or chemical syntheses) for fun. Go to at least one free dance lesson. That sort of thing.

If you get into Harvard, you should accept. Figure out a way to pay for at least a semester. Even if you drop out, you still went to Harvard, which carries more weight than graduating with honors from some fine schools.

It's often good advice, other things being equal, to go to the best school you get into. Of course, other things are rarely, if ever, equal. (Where best means most prestigious.)

The Harvard name, particularly internationally, is probably without peer among U.S. institutions. On the other hand, I think it's at least possible that for certain fields, including engineering, that an MIT degree, for example, would be viewed just as positively among those who are most likely to matter in terms of career advancement, etc. But people in engineering could speak better to that than I.

It's also my impression, based on conversations with friends who are alumni of the school, that one of the primary criticisms leveled against Harvard is its lack of focus on the undergraduate school as opposed to the grad and professional schools. One good friend of mine, while very happy to have the Harvard name on his resume, was somewhat disappointed in the academic experience at Harvard because of that. Of the schools I'm most familiar with on your list, Swarthmore, for example, would be the very opposite of Harvard in terms of its attention to the undergrad experience.

I do interviews for my undergrad college, and always advise people, once they've narrowed down their list using whatever criteria they've determined are most important to them, that they won't go wrong by going with their gut in choosing among the remaining contenders. Maybe that doesn't sound like rationalist advice, but again, this is after you've already applied your rational analysis and narrowed your list down to just a handful of schools. (Of course, your analysis may leave you with only one school on your list anyway, in which case, no need to resort to the gut.) At that point, I recommend going with your gut, particularly if your gut feeling is informed by visits during admitted student events, which I highly recommend if you can swing it, and which, while not giving you perfect insight into the school, give you a different way to evaluate than just comparing schools on paper. Talking to current students and alumni is also useful.

I faced a similar choice last year. I was accepted to Princeton, MIT, Rice, Georgia Tech, and the University of Rochester; I am now going to Rochester.

For me, an important consideration was whether I would be an average student or an exceptional student at the college. This may sound petty and shallow, but I think I would be unhappy and unmotivated if I were not a top student at the college that I went to. Here at Rochester, I am the top scoring freshman in my courses and math competitions, but had I gone to Princeton or MIT, I would probably be an average math student; certainly not exceptional (this can verified from previous Putnam Competition results). Of course, you may have an opposite personality to mine. Perhaps you are more motivated if you are not already a top student.

I think you should also consider whether you would have more opportunities as a top student at a second rank university, or as an average student at a first rank university. Some people say that you get a lot more academic and research opportunities by going to a first rank university, but I don't agree. Certainly, the average student at a first rank university will do more research than the average student at a second rank university. But remember that by going to a second rank university, you will not be an average student.

Of course, there are other important considerations. The points I mentioned here are those that I consider important, but haven't been mentioned yet.

Disclaimer: I go to MIT and am probably biased.

I think the set {MIT, CMU, Harvey Mudd} dominates all the other places you are considering. Roughly speaking, MIT/CMU are the clear best in terms of academics, but if you are worried that the academic programs would be too difficult for you to have time to explore other topics on your own, then Harvey Mudd is a more laid-back school that still has good academics and the sort of quirky student body that might appeal to LWers.

I will also note that MIT is probably unique in terms of the ease with which undergraduates can do research.

In more detail: first, you almost certainly shouldn't go to Harvard. Harvard is an excellent school, particularly in terms of theoretical math and physics, but it doesn't focus much on engineering. You also probably shouldn't go to USC, UMD, or Swarthmore, because the only reason to choose those over MIT/Harvard would be to have an easier degree program, which Harvey Mudd provides while having a better academic program. Note: I am not completely sure of this statement, look up the relative rankings of engineering at USC, UMD, Swarthmore, Harvey Mudd yourself to make sure.

In terms of overall strength of academics as well as student body, {MIT,Harvard} are better than the rest of the colleges you listed, with CMU comparable enough to not rule it out entirely on academic grounds. As I already noted, Harvard is not an engineering school, which rules it out. Therefore, if your goal is to have the best engineering education possible, and to be surrounded by the brightest possible group of peers and instructors, you should go to MIT, or possibly CMU. Further, if undergraduate research is important to you, this is a further reason to consider MIT.

The only reason to not go to the best school possible is because better schools probably have more difficult classes, which might give you less free time. I personally have not run into this issue except by my own volition (I'm currently taking five classes, play sports, and spend 10+ hours/week on research; you only need to take four classes/semester to graduate on time). However, I could imagine this being a problem, especially if you come in without much background and choose a major with many graduation requirements.

The question then becomes how to determine if going to a top university would be an enriching experience or just suck up all your time for 4 years. For this you may want to consider your current background. Are you generally mathematically mature, or will you spend your first semester taking introductory calculus? Do you know at least one programming language? Can you pick up new information quickly? Have you taken at least a couple AP science courses? If you answered yes to all of these, you're probably reasonably well-prepared for any university. If you answered no to all of these, then you probably would not have a good time at the most rigorous universities like MIT/CMU. If it was a general mixture, you could get an improved estimate by looking at typical classes on OCW and seeing if the pace is reasonable or not.

Finally, please don't underestimate the relevance of being able (at a top research university) to interact with the world experts in most fields, as well as extremely bright students. I've discovered numerous academic gems through conversations with these people that I would have been unlikely to get by participating in online communities or reading papers off of google scholar (including entire fields of study / research programs that I didn't know existed).

A general suggestion is to not put too much emphasis on money. The good schools will work with you, and if you demonstrate financial need, they will shoulder at least some of the burden.

Furthermore, student loans may seem scary, but graduating from a top tier school with loans is often preferable to graduating from a more mediocre one in the black, because your earning potential will be that much greater. There are websites that track graduate salaries according to alma mater. The difference is often quite large, even more so when you consider how it adds up over the years.

Plus there are all the intangible benefits you will obtain from the more prestigious institutions. Access to world-class faculty and facilities, beneficial social opportunities while on campus and alumni networks afterwards, the brand name of the school, etc.

What do you mean by flexibility?

If you are interested in grad school and money is a concern, a good strategy might be to go to the subsidized state school, zip through in 3 years, then go to grad school at a big name place.

Don't forget to consider the weather.

What did you eventually decide, and why?