Kodama Sushi. 45th & 8th. Not fancy inside, but delicious and reasonably priced sushi and sashimi. They cater to the pre and post theater crowd. There is always one table of Japanese businessmen, which I consider to be an excellent sign.
Joe Allen and Orso on Restaurant Row are always good. Nearby on Ninth, Breeze (Thai) and Hell's Kitchen (Mexican). Just slightly farther but very good are Chimichurri Grill and Bocca di Bacco. I probably wouldn't head east of the theater for dining.
Bryant Park Grill is a lovely setting between w 40th and w.42 behind the public library facing the square; Cafe Un Deux Trois 123 West 44th Street, New York, NY 10036 (212) 354-4148 ; Orso is on W46th mentioned above, open fire brick oven Love 44 and x mentioned above, further to west if game for it.
Haru on 43 St. Nice Japanese place; have eaten there often Cafe Un, Deux, Trois 44th Street (nice brunch) very popular Playwrights (44th & 8th)--not fancy but decent value; eat upstairs, not in the bar area
Joe Allen is a classic. Haru is also very nice. Personally, I'm partial to going west from Times Square, so I'd cross anything east of 7th off my list, but that's just my bias. Unless a person has mobility issues, or the weather is absolutely dreadful, I don't think 10th Ave is too far a walk from the Richard Rodgers.
Depending on size of group and ages, Ellen's Stardust Diner (B'way and 51st) can be a huge hit -- food is serviceable, service is quick, but it's the singing waitstaff sharing showtunes which make it sparkle. Lines move quickly, particularly for parties of 2 or 3 --
We ended up at a place called Il Forno - corner of 8th and 45th. Good enough food and plenty of seating which was important because we were running a bit late. The mushroom risotto was very good. I like the margherita pizza as well.
tjohn