I'm a fan of Bin 228. A bit more informal than the more expensive ones mentioned above, but nice, small, low-key and I've always had good, attentive service (and they remember stuff from visit to visit, which, as an out-of-towner, is impressive to me). Nothing earth-shattering, but nice wine list and lots of small plate type choices that can be fun for a date night. 99% of the time when I am there for lunch I get the "meatball salad," which is not on the menu, but so many people order it that they know what you're talking about when you ask for it (exactly what it sounds like, meatballs on a salad--arugula iirc--with toast points). Fondue is good and fun, too.
If you want something with more of a downtown buzz (to the extent Hartford has one), I've also had good meals at Max Downtown, Salute and Feng Asian Bistro if you like sushi.