Depending on the timing of the trip, if you are in Cleveland during the day, I would stop at West Side Market. It's off I90 and has a very wide selection of food vendors among other things.
But I think you should DEFINITELY try out:
Siam's on St. Clair. It's not Eastern European, but it's some amazing Thai food.
Little Budapest is nice as well, but not very scenic.. good Hungarian food. Balaton is also pretty good. It's named after the Lake Balaton, which is a great vacation spot!
Surprisingly, Cleveland has a TON of great ethnic eateries. Oooh and I'd suggest trying out some Middle Eastern / Puerto Rican eateries as well since they have a LARGE presence on the west side of Cleveland. But I doubt you'll have time for all that
