Batman has about eighteen different back-stories so I'll just focus on a couple.
In the comic series "Night of the Stalker" (originally appearing in 1974 in Detective Comics #439, we see that he has a diploma on his wall. Closer inspection reveals it to be from Yale University of Law.
In Batman #93 (in a segment called "Batman's College Days") we learn that he has a degree in Criminology from Gotham University
And in Batman Begins, we see that young Bruce is on the verge of dropping out of Princeton University:
ALFRED : Will you be heading back to Princeton tomorrow or could I persuade you to spend an extra night or two?
BRUCE : I’m not heading back at all.
ALFRED : You don’t like it there?
Bruce smiles, sardonic. Looks out at the trees flashing by.
BRUCE : I like it fine... they just don’t feel the same way.