I'm from there. "Vintage Vinyl" is the best overall record shop I've ever
been to. It used to be 2 stores but one closed, leaving one with twice
the stock. I have no idea how to get there. I never had a car when I
lived there and never paid attention to how to get around. VV does not
specialize, but has lots of everything.
New Brunswick has many good record shops, being a college town and all.
Rockaway Beach in Point Pleasant is a tiny tiny shop but the guy who works
there is nice enough and he'll order anything. that won't do you much
good.
As for things to "do"....ummmm, ummmm.... the boardwalk I guess. I used
to walk around the woods a lot. The roads are insane, so you can get lost
a lot if you so choose.
Depending on where you'll be, you'd have a better time in NYC or Philly.