My wife love's to eat at Old Lviv, but you may need to know what to expect first. The first time we went there, we weren't even sure if it was actually open, and that impression hasn't left the 2 or 3 other times we have gone there.
The place is extremely small, with a bar and just about 2 or 3 tables, and has always been empty when we have gone (typically weekend nights). In the back is the steam table where she always has a buffet going. "Old Lviv", or whatever her name really is, is always hanging around, talking to someone or just reading, and she will take your order.
Note that as far as I remember, the only thing you can actually order is the soup. I have had the chicken noodle, which has those long, thin noodles I think that used to be in the dry boxes of chicken soup you could make at home (was it Lipton's?), but now add a very good chicken broth and fresh dill to it. The beet soup was also excellent.
The rest of the meal has been at the buffet table (perhaps you can special order, but I don't recall). Often the cook starts prepping new things when we arrive, and those are usually very good. It is somewhat typical Eastern European fare (I think the food is Ukranian), and I remember liking the stuffed cabbage, the blintzes and perhaps the ground pork patties. Oh yeah, and the carrot and beet salads. And I think the entire buffet (including the soup) is under $8 or $9.
If you live nearby, it is at least worth a visit for the soups alone.
"My doctor told me to stop having intimate dinners for four. Unless there are three other people."
-Orson Welles-