If you want an eclectic experience: CAV

If you want a decadent experience and cost is no concern: Gracie’s; if cost is a concern: Siena

If you want a bar/pub food experience: The District

If you want an old world experience: Camille’s

If you want a REALLY old world New England experience: The White Horse Tavern

There are a hundred other great spots to go to ranging in price and cuisine and such. But those are a good range above to start with.