Man, 4 tomatoes from one cherry plant in a 5 gallon bucket is on the low side but it happens a lot on balconies. The big question is what kind of soil you used, because if it was straight potting mix with no slow release fertilizer that plant probably ran out of food right when it started setting fruit. Cherry types usually want a good amount of calcium and steady water or the flowers just drop before they turn into tomatoes. Also, how many hours of direct sun was that bucket actually getting after you moved it to the east side? East light is gentler but it's often only 4 or 5 hours, and tomatoes really want 6 to 8 to pump out fruit. Did you see a bunch of yellow flowers that just dried up and fell off, or did the plant barely flower at all? That answer would tell you if it's a food problem or a light problem.

My buddy Dave did the same thing with peppers from a farmers market in Charlottesville two years back, saved seeds from a red bell he bought and ended up with four plants on a fire escape that got maybe 6 hours of sun. Two of them grew into something totally different than what he started with, kinda small and thin skinned, but the other two were fine. Peppers cross pollinate pretty easy if there's other stuff blooming nearby, so you never know what you'll get. Worth trying since the seeds are free, just don't expect them all to taste like the ones you saved from.