Lithuanian food is predominantly meat and potatoes, but they have an excellent range of recipes. If you want some traditional Lithuanian fare and beer, try restaurant 'Zemaiciu Smukle' on Vokieciu 24 in the middle of the Old Town. There is street-level outdoor seating in the summer months, and downstairs a maze of rooms, caverns and bars. The menu is in Lithuanian, so take VIYP to decipher it.
There are plenty of pizza, Mexican, and Chinese restaurants, but try the local restaurants with local cuisine--they really are unique, and choosing from the menu can be quite an adventure. If you want Lithuanian food, but an English menu, try Amatininku Uzeiga on Didzioji 19/2. They really have a great celery-and-radish soup and fantastic beer.