Can I get to, say, Yale Grad School given that I'm 20, speak 4 languages and that I'm most likely graduating magna cum laude with a diploma in Linguistics? On the other hand, I'm not a US citizen and I don't really have much money. From what I've heard, only children of famous politicians, scientists, lawyers etc can get there
If you can dream it, you can achieve it - up to you !!...go get 'em !!
First of all, what university you choose should depend on what you want to study and whether that university is particularly famous in that field.
Secondly: Yale and all private universities in the US cost a lot of money. Not to be admitted - forget the bit about famous politicians and all that - but once you're admitted, the tuition fees as well as the cost of living is very, very high.
That's where things like Fullbright scholarships and other scholarships come in.
So - forget about the 'name' as such, and find some good universities that are known for the subjects you want to specialize in. Contact them about scholarships, and contact your US embassy or consulate about Fullbrights.