You realize, of course, that often no wait especially during peak times often means that the food is not as good as other places. Sometimes the food really is worth the wait.
However, there are also many neighborhoody places that the general public doesn't know about or is out of the way.
1) Miracle Grill - the restaurant Bobby Flay used to work at before he opened up Mesa Grill and became the Food Network celebrity that he is now. Great Southwestern food - not horribly expensive. If you like pork chops get their pork chops - enough to split the meal between two people. And the one on 1st Ave has a backyard outdoor area - very nice during this time of the year and during the summer. 1st Ave between 7th and 8th I think.
2) La Paella - Spanish/tapas restaurant on 9th St between 2nd and 3rd Ave. Sometimes there is a little wait as they don't take reservations and the college crowd likes to go there because it is relatively cheap and has fantastic sangria (my favorite sangria in the city). The decor is nice especially for a date as it is cozy, dimly lit and even has a charcoal drawing of Don Quixote tilting at a windmill on the wall. Their signature dish is the paella, but I usually opt for the tapas - good portions and usually only around $6-7 a plate. Usually no wait for 2 people, but sometimes a wait for more people especially during peak dinner hours on the weekends.
3) Takahachi - a neighborhood Japanese restaurant in Tribeca on Duane St betwen Church and West Broadway. Everyone knows of the more famous Japanese restaurant in Tribeca (Nobu) and other famous restaurants down there (Tribeca Grill, Bouley, Chanterelle, Dylan Prime for example), but this place is one of the hidden gems of the neighborhood that has so many good restaurants (check out Taste of Tribeca on May 20th - do a search and see what its all about). The food here is wonderful with incredibly fresh fish if you like sushi and sashimi but also great dishes out of the kitchen. A lot of seasonal and weekly specials that are much different than your regular sushi, teriyaki and tempura. I remember having this one special there - squid ravioli - thin slices of squid with uni filling (sea urchin roe) - that was incredible! You would think it really tasted like a ravioli except that much more flavorful. Or the Salmon Party - a dish of salmon sashimi except it has many different kinds of salmon (red salmon, white salmon, wild salmon, alaskan king salmon as well as the regular variety salmon). Each kind of salmon looks different, has different textures and different flavors. Pick a couple of these small dishes and share for the best experience. As the people who live around there and they will all say its great. The head sushi chef is an older Japanese guy who is incredibly skilled. He knows exactly which piece of the fish is the most tender and each piece is sliced perfectly! I've been to Nobu and Blue Ribbon Sushi - this is definitely the best especially for the money!
4) Petite Abeille - Belgian restaurant chain in the city - one in Tribeca on West Broadway and Duane, another in Chelsea on 18th St off 6th Ave - I think there may be one more place. Not pretentious at all like Markt and the prices are great. Wednesday night is Moules and Frites night (mussels and fries). $16 gets you all-you-can-eat mussels with different sauces and a glass of Stella Artois (beer if you are unfamiliar). They have an incredibly good burger as well as a wonderful Flemish beef stew and a Belgian version of a chicken pot pie. All under $15 per selection. And the portions are good. That leaves plenty of fiscal flexibility to get a glass of Belgian beer from an assortment of breweries (if you like beer and have never had Belgian beer - I highly recommend it!).
Best thing in general is to avoid the touristy places as those will usually be overpriced and overcrowded (of course there are exceptions such as Mario Batali's Lupa on Thompson between Bleecker and Houston - always a wait, but entrees are no more than $15-16 and the food is wonderful). As the locals of any neighborhood where they tend to go - that will give you a good idea of where the good places are. Check out the Time Out Food and Drink Guide or Citysearch. Those will give you wonderful ideas of where to try. That's how I got started, especially with a much more limited budget back then.