Found a small Ukrainian restaurant in Clifton called Cafe Restaurant Lidia, in the Botany Village neighborhood. It's only been around for a few months.
For lunch, I had red borscht, stuffed cabbage and blintzes for about $10, and all were very, very good. There's no written menu, and Lidia tried to explain what she had that day, but there was a bit of a language barrier, so I just nodded and she brought out food. The place is very small, with only three or four tables used on a regular basis. (The others are pushed against the wall, apparently used for parties on weekends.)
Also, I know there's a sizeable Ukrainian population in Clifton/Wallington/Garfield, but this hasn't seemed to translate into Ukrainian restaurants. Does anyone know of any others?