Here are three in downtown Princeton that you might like:

1.   Blue Point Grill, 258 Nassau Street.  Seafood place with good selection and many daily specials based upon what's fresh at the fish markets.  BYOB. Doesn't have a bar so you will need a table if you are dining alone.  Fills up fast so call for a reservation.

2.  Witherspoon Grill, Witherspoon Street, next to town library one block of Nassau Street.  American contemporary with a big bar that seems to have fairly mixed crowd of townies (Princeton variety) young professionals and maybe some younger faculty.  Great martinis and bar staff seemed friendly.

3.  Winberries. Palmer Square just off Nassau St.     More casual, college place with good bar food, plenty of bar seats and many tables. Will fill up on weekends and probably on Wednesdays etc.    

As an aside, Princeton was never seen as a good food town.  The best Italian food was in the Chambersburg section of Trenton, which 30 years ago had a dozen top quality Italian restaurants.  All have closed or moved to the suburbs, mostly Lawrence Township which is not far from Princeton's Route 1 corridor, but you will need a car or a cab. I would have to do some research to find them now, so I tend to go to a few places that I know.