I would try Chez Piggy for interesting and great tasting food. Wooden Heads for wood fired pizzas. There is a great Vietnamese place on the south side of King Street between Princess and Brock... sorry can't remember the name.. and the Brew Pub on Clarence is a great place for beer. Kingston isn't too fancy as a rule and service is usually fairly casual.
192 Ontario St, Kingston, ON K7L2Y8, CA
Le Chien Noir for food, not sure about beer.
Kingston Brew Pub and Tir Nan Og for beer, ok pub food.
Pan Chancho for a nice lunch and great patio, esp. on this nice weekend.
The Wok In on Montreal St. for cheap, amazing Thai food (unlicensed, so get take-out).
I haven't been there since the summer, so I'm sure there are more recent recs, but these are pretty solid. (IMHO)
69 Brock St, Kingston, ON K7L1R8, CA
Tir Nan Og
200 Ontario St, Kingston, ON K7L2Y9, CA