I'm not the OP but I'd love some suggestions. We go to NYC every Fall and are always looking for new places (to us).
I have a few suggestions for the area....
I love chef Julian Medina. He owns Toloache (on 50th and 8th, plus a few other locations). However, it is not cheap. He also owns Tacuba in Hell's Kitchen and Astoria. It is also excellent, but cheaper. I can just taste the grilled octopus and chorizo tacos.
Toto Ramen (a couple of locations around 51 & 8th) - Cheap, but wow. There is nothing like the Chicken Paitan Ramen.
Pizza - There are so many places, but 99.9% of just ok. I would recommend Starita's Don Antonio (50th and 8th). Only 2 locations in the world. NYC and Rome. They have pictures of the pope eating their pizza. It a pie place, not a slice place. Cheap as well. If you really want a cheap slice, I sometimes get the $1 slice at the pizza place at 8th and 43rd. It is near the Port Authority, so if I am hungry on the way home it is convenient. No different than most of the other $3/$4 slice places.
Tapas - really like Boqueria on 8th and 40th st. Short walk to MSG. Go there and get the chefs tasting (or what ever it is called). Probably about $100/couple without tip or alcohol. What a great meal!
Palm at 50th and 8th (not a fan of the one in Tribeca) - The food is pretty solid, but very expensive. However, they have a nice lunch special. I think it is upper 20s for 3 courses. The Lobster Bisque at the Palm is the best I have ever had. Usually they will let you substitute it for the first course. Even though it is a steak house, their chicken parm is outstanding (and on lunch special).
Mark Forgione's American Cut in Tribeca. I am usually not a fan of steakhouses or celebrity chefs, however this steakhouse has some really unusual takes on typical steak house fare. Their everything biscuit that they serve as bread with a vegi cream cheese spread is just typical of how they are different. Pretty Expensive though.
The Breslin in the Ace Hotel on 29th st has a famous lamb burger with triple fried duck fat French fries. It is really good and not too expensive.
Overall, there are lots of expensive restaurants in NYC, many of them are just OK. I would recommend trying to find ones that have good happy hour deals and eating at the bar.
Joe