In the way that Fortune City in Dead Rising 2 is a parody of Vegas, which makes no sense because Vegas also exists in that universe.
Oh.
Well in some ways it is, and in some it isn't. The culture is just very...New England, in general. If anything I'd say it's a spoof on that and not one specific city or state.
The accents in the show are typical New England ones, but not everyone has them. For example, in my area, a lot of us don't talk like that (I certainly don't.). But if you go to Warwick or Providence...yeah. You're going to get the BAWSTON accent.
Quahog (the town) doesn't actually exist. If it had a real life counterpart, I'd have to say it's similar to Naragansett.
But it does actually feature specific RI locations. Lois, for example, is an alumni of my university. It was even featured in an unaired episode (because she ends up getting an abortion).