Not Europe, but...
Doesn't SF have a decent art school? You'll do quite well in any reputable university, I would think - UCLA or USC for instance.
I went to
The University of the Arts for painting and drawing, so I can't comment on their design school (they offer graphic design and industrial design - the guy who wrote "Making and Breaking the Grid" went there), but overall it was a good experience. Philly's a great city, too, if you're into the east coast thing.
Other good east coast schools...
RISD (Rhode Island School of Design, pronounced "rizz-dee" usually)
MICA (Maryland Institute College of Art)
SCAD (Savannah College of Art and Design - Georgia's climate is more akin to California, too)
In New York, there's always Pratt, Cooper Union, NYU.
Avoid "Art Institutes International". They suck - they're the McDonalds of art schools.