There is no New Haven tradition finer than Claire's cakes. My favorite is the Lithuanian Coffeecake, but the carrot cake and chocolate varietals are divine as well. It's all about the frosting, that incredibly light and creamy vanilla buttercream (light refering to texture, not caloric content...it may be pure fat. But who cares?).
If you get past the cakes, (although really, why would you? Have the cake. For lunch. Or breakfast. Or dinner. Why not?) Claire's has a wide variety of vegetarian options, some in a Mexican style, some in an Italian vein, all filling and tasty. The service is friendly and accommodating, if not particularly fast, and there's frequently a local artist exibiting on the walls.
As a bonus, being an exclusively vegetarian restaurant, Claire's is certified Kosher, if that concerns you or one of your dining companions.
It's also right across from the Shubert, so if you're having lunch, you're likely to see some of the cast members of whatever touring broadway show is in town at the table next to yours.