Curtis is probably the most difficult music school to get into in the world - they accept about 4 or so pianists per year. However, a lot of fees you would normally pay at another school is subsidized by Curtis and the numerous foundations that endow that school. They even give you a S&S grand for your entire tenure there. Also, you can study with just about anyone you want.
Curtis has not had a great track record of producing great pianists over the last few years. The most well known recently is Lang Lang - need I say more.
Juilliard is very difficult to get into, as well.
Aside from that, there are other great schools in the US - Cincinnati Conservatory (best kept secret in the US), Indiana, Oberlin, numerous schools in Texas, etc., etc., etc.
I guess it depends on what type of musical education you want. The criticisms people often have with Juilliard and Curtis is they are geared to produce performers, and not necessarily well rounded musicians.
Also, the most important consideration is not the school, but who you will be studying with. Start thinking about that now, and about developing connections with some prospective teachers.
Location is an important consideration - US cities, UK, etc. New York - where Juilliard is - can be a tough town, with a lot of distractions, and is very expensive. Travelling to another country is a great idea, but I would do it for one year and not four. A lot of college students do one year abroad at - say - the Wiener Hochschule fur Musik, or one of the other good European conservatories. I would not live for four years in any country - even the UK - without having spent a good amount of time there. I had a chance to move to the UK, and turned it down because it's a nice place to visit, and a great country, but I wouldn't want to live there.