Klaipeda's, if not Lithuania's, most distinctive restaurant is Skandalas at Kanto 44.
This is a bit of a hike from the town centre but is well worth it.
This American-style restaurant is a massively OTT shrine to Americana, with it's statues, photos of film-stars, flags, assorted bric-a-brac, and most obviously the telephone installed in a black caddy (as in car, not golf, obviously) installed in the lobby. The food is great, and although the prices are slightly high by Klaipeda's standards, by Western standards it is cheap. I can recommend without reservation the huge steaks; I had one of these and 4 or 6 beers and it all came to less than £15.
Skandalas stays open until the early hours but it can get very busy; if you get there before 7pm the food is cheaper too. Try and get a seat on one of the swings suspended from the ceiling. You can also get imported beers here, including Guinness, but with the quality of Lithuanian beer, why bother?