I'm way too familiar with restaurants of New Haven. I'll just give a few highlights before OhDenny gets here!
First off, New Haven is known for their
apizza. The three most popular are Pepe, Modern and Sally's. Of these three I like Modern the most, but my absolute favorite is a mashed potato, bacon, and garlic pizza from
Bar. If you want a traditional apizza, get a white clam pizza from Pepe.
My favorite restaurant in general is
Caseus. It's owned by a dude named Sobocinski who knows everything about cheese. He travels all over the world to find the best cheeses - he's even been on the Cooking Channel to talk about cheese. Him and his brother run it and opened up a new bar called Ordinary as well.
Miya's Sushi is a great non-traditional sushi place. They're about sustainability, local, blah, blah, and have interesting variety of sushi, such as curry and cauliflower. Great choice in drink is their Chinese firecracker sake.
Other great restaurant choices include Barcelona, for Tapas and wine, and
Zinc.