If I tell people that I go to this school...?

If they are impressed by students who study at top graduate programs, they will be impressed.

I'd say "okay". I know Georgetown is a great school, but I don't believe in fanning anyone's ego. You could go to Harvard and I would still say "okay".

If it is a top university then yes

It is mainly the grades that will make you look good
The university will just be a benefit