Hi!
hey, it is hard to answer a general question...
CEU is a small but good university by european standards, I believe it would rank pretty well in the states as well, but you have probably researched that yourself. It feels and smells like a good (private) university in some anglo-saxon country, I am nearly sure that international students make up much more than half of the population - in other words there is not too much connection between CEU and the rest of Hungarian higher education, it nearly feels like a different country (there are some Hungarians working there, occasionally.)
And, my friend who sometimes teaches there says, students have to work rather hard there...
From the prospective of someone having lived in Western europe but not the US:
With 2.5 inhabitants including agglomeration, Budapest is quite a vibrant city (I am biased but have seen a few cities)
Smaller than SF (surprized?) but reasonably large within europe (I think ranking around number 8 acc.to official statistics, larger than Prague, or Amsterdam, smaller than Berlin, similar to Hamburg... quite exactly the same size as Vienna, but feels younger, imho, and also more bancrupt... ).
Well, I can tell, hungarians are significantly different from germans, and even austrians, after all.
I think it is safe to assume that, like many other European cities, Budapest must feel different from home to a US person in many aspects, e.g. it is still (at this point) safer, much easier to live without a car, full of cultural opportunities (e.g. classical music) - and less multicultural than any reasonable city in the anglo-saxon world. But you will have CEU for that, The expat population has been steadily growing since the EU joined Hungary(or was it otherwise?), and includes many hundred medical students paying their asses off in Semmelweis Uni:-)
Being in eastern Europe, Budapest should feel rather cheap for you, as you can see from many threads of the type "can I live on that salary?".
The downside of eastern Europe is that some infrastructure is not quite as good as, say in Vienna. Some form of corruption is more widespread (you may not meet it though). Public health care is so-so, but you wont die on the street for lack of many(perhaps next year).(You can probably afford private health care here, not sure how that works tho).
Also, people speak less english (While not the main reason, it IS harder for a hungarian to speak good english than for -say- a german, believe me), and are generally slightly less travelled for financial/political?/ reasons (compared to Western Europeans, no idea about US). However, for below 30s all of that is much less true. Anyway, you won't starve here without hungarian knowledge for sure. (But hey, ever tried to get around in SF with german or French, or Hungarian? Â
Of course US-expats on this list can tell you much better how Budapest feels for an american.
Any perhaps slightly more specific questions?