A few years ago I enjoyed visiting “A taste of Lithuania” (Lietuviškas Skonis) just off the cathedral square near the Amberton Hotel on Odminių g.
It was a family run cafe bar which made very nice fresh food, provided free wi-fi and sold some nice souvenirs. (See my earlier post on it). They also had a shop at Vilnius airport for a while.
Whether it will still be there next time I visit is anyone’s guess.