Also, the most famous of those universities (MIT and Harvard) are in Cambridge.

Someone from outside Boston might look at the entire metropolitan area and call it "Boston", but one of the key elements of the movie is that Will and Chuckie are locals who are living their entire lives in a small neighbourhood in South Boston.

For a local, there are huge differences between Cambridge, Somerville, South Boston, the North End, Beacon Hill, Charlestown, East Boston, etc.

In any case, in the movie he never says "you've gotta get out of this town and make something of yourself". What he does say is that the best 10 seconds of his day is when he walks up to Will's door and hopes that he'll have left without saying goodbye. That does suggest that to fulfill his potential he'll have to move somewhere else, at least for a while. But, the way the lines are delivered, it's not that he has to leave the Greater Boston Area, but that he can't just get stuck in a rut, living in the same place, doing the same thing, never taking a chance to improve his life.

Sure, theoretically Will could live in the same house for the rest of his life, while also making the most of his talent by working at Harvard or something and just commuting from South Boston. But, the other context for that scene is the girlfriend.

Chuckie asks Will about his girlfriend, and Will says she's moving to California to go to med school. That's what kicks the whole scene off. The audience knows that Skylar invited Will to come with her, and not only did he turn her down, he basically had a panic attack at the idea of leaving his life in South Boston. Chuckie knows Will well enough to know that it wasn't just a casual fling, and he's happy to end it because she left town. At the end of the movie, Will's friends give him a car for his birthday, and he uses the car to drive to California to be with Skylar.

Now, maybe in 10 years he'll move back to the greater Boston area, get a job at MIT or Harvard, buy a house next door to Chuckie and commute to his job from his old neighbourhood. Maybe his and Skylar's kids will play little league games together, and the two will hang out to watch the Patriots (and they'll be in for a hell of an era for that team). But, even then, he'll have done what Chuckie wanted and not waste his talent.

The scene has nothing to do with leaving the Boston area to get a good intellectual job, and everything to do with not getting stuck in a rut, being scared to take a chance and use your talent.