For reference you can drag to 37th Minute in the movie where Bruce is talking to the security guard (Lou Ferrigno) inside the campus.
The clip in question is seen early in this video. Edward Norton doesn't do much talking, but from what I can hear, he is speaking in his normal voice - a generic American accent, except perhaps for a subtle, slightly East Coast tinge, like a very mild New York accent. This is barely noticeable, and can only be picked up in the occasional word or two. There is no distinct or recognizable regional accent - no southern drawl, no West Coast surfer twang, no hokey Midwestern warble, no bellicose New England dropped "r", no pronounced accent of any kind, really. The only slight trace of an accent is, as I said, a tiny hint of a Mid-Atlantic, vaguely Northeastern, mild, possibly New York accent.
It isn't clear if, or why, he would deliberately choose to use a Northeastern accent, since the scene in question is set in Virginia. We might assume that either Bruce is trying to pose as an out of state student at the University (which is where he encounters Lou Ferrigno) working part time as a pizza delivery boy; or alternatively, that he isn't trying to put on an accent of any kind.
Out-of-universe, Ed Norton was born in Boston, but raised in Maryland. It seems that he left Boston when he was very young, and so didn't pick up the trademark Boston accent. But he also doesn't have a Maryland accent, which is slightly Southern in nature. He decided to become an actor when he was only 5 years old, and probably learned to speak without an identifiable accent of any kind, which would help him get more roles and make it easier to adapt to whatever accent a particular role required. His normal speaking voice is, once again, vaguely (mid- to Northern-) East Coast, but not especially pronounced.