Bistro 60 (60th St. between Park & Madison) is good and very convenient to 59E59 theater...you can actually walk through the Alliance Francaise mid-block and end up at the theater on the other side. When I went, there was actually a special deal for a very inexpensive prix fixe menu on the ticket envelope.
37 E 60th St, New York, NY 10022
I've always been a fan of David Burke Townhouse on 61st between Park and Lex. I just find it well priced for the area in terms of food and surroundings. Signatures include a tuna and yellowtail parfait and a short rib with cavatelli and mushrooms that would suit both the sushi and italian interests.
Since my office is in the neighborhood, for a moderate priced restaurant I strongly recommend Ma Peche. It's a perfect pre-theatre restaurant (I've gone there for my pre-theatre dinners). The cuisine is French-Vietnamese, but more important, the food is delicious.
15 W 56th St, New York, NY 10019