I live in New Haven, and these are places that people have to try in the city:
1. Skappo - Italian/Wine Bar. Phenomenal food and wine selection, and the menu changes daily.
2. Zafra - Cuban/Rum Bar. Best Cuban food in the state, along with over 200 different types of rum available. I'm a big fan of mojitos, and they have some of the best around.
3. Ordinary - Hipster bar with a limited menu, but they have hands down one of the best grilled cheeses I have ever had in my life. Cool vibe, good beer selection.
4. Prime 16 - Cajun Patty Melt...
5. Consiglio's - on Wooster street, its the kind of place that the mafia would eat at (in a good way). Dated décor, but the food and service was awesome. Highly recommended
6. BAR - Pizza...and a nightclub
7. Soul de Cuba - Pan con Bistec
8. Anna Liffey's - Great for football (European) on Saturday mornings, if you are looking for a full breakfast, bangers & mash or your typical garbage plate. Surprisingly, they have a full dinner menu too including Philly Cheesesteak Eggrolls and typical Irish fare.
9. Caseus - Cheese shop with a creative menu