Tartine in West Village has 2 kinds - one in Bordeaux Sauce and the other in Peppercorn-based sauce. The steaks are decent and the sauces are pretty good and the fries are better. I think, each is under $20. BYOB, to booth.
There is Père Pinard on the Lower east side....Chez Jules on St-Mark's place....Brasserie Les Halles....L'express....Chez Lucien...Those are the ones I have tried and they are good. I would say that Lucien is the best.