It's not like Maine, where your choices are virtually infinite. We're Up Islanders (meaning that we avoid the towns), so we get our rolls at The Galley or Larsen's in Menemsha. Pretty good frozen custard at The Galley, too. We've gotten lobster rolls at some hoity-toiter joint in Edgartown, but I think the Galley has it beat (plus, I can't remember which one -- maybe the Navigator?). I don't know if Net Result has lobster rolls, but they'll be pretty good if they do.
some other foods not to miss:
Fried Clams from The Bite in Menemsha
Pies from Back Alleys
Anything from Morning Glory Farm on the road between Edgartown and West Tisbury
Noodles from the West Tisbury farmers market (Saturday morning and Wednesday afternoon)
Oysters on the back dock from Larsen's