Alas, inexpensive food is hard to come by in Manhattan but not impossible.
If you are in the Times Square area and don't want to eat at a chain, try Emmett O'Lunney's on 50th just off Broadway. The food is good and, for the area, reasonable. But that still means a $15 burger. If you go there, tell Emmett that the Karen the knitter sent you. We always go there after Vogue Knitting.
One of the least known great deals in NYC is Becco's Sinfonia di Pasta. http://becco-nyc.com/menus/#dinner $25 bucks for three different kinds of pasta, Caesar salad and antipasto. And they bring seconds. And thirds. They also have a $25 a bottle wine list. Considering that wine can easily run $12 a glass in Manhattan this is a fantastic deal. Becco is a Mario Batalli and Lidia Bastianich restaurant. The downstairs is always packed and lively. Upstairs is more serene. Make a reservation now if you want to go there.
Sylvia's in Harlem is always fun. The food is good and the price is right. A real New York joint. Try for Gospel Sunday. http://sylviasrestaurant.com/menus/ I would make a reservation here too.
Take the subway out to Astoria for fantastic middle eastern food. If you don't have an adventurous palate, don't worry. There is something for everyone.
Chinatown. Always look for the restaurant with the most Chinese people eating in it. There's a really good dim sum place under the Manhattan Bridge.
If you want to leave the city but not go too far, try X20 in Yonkers for the Dylan Lounge specials. It is literally steps from the Yonkers Metro North train. Under $30 for a three course meal. The restaurant is on the second floor of the Yonkers City Pier so the Hudson River experience is fantastic. Peter Kelly is an amazing chef (he kicked Bobby Flay's ass on Iron Chef which made me very happy because I loathe Bobby Flay). He is also one of the few super high end chef's who have made a deep commitment to front of the house diversity. The staff genuinely reflects the people who live in the area, he brings much needed wages into the area, and it is some of the finest service I've ever enjoyed. Call ahead 914-965-9100 to find out what's on the menu. Plan it so you can have cocktails outside at The Dolphin's outdoor bar. (And let me know if you are going there and I will meet you for a wine.) X20 also has a fantastic Sunday brunch. Three courses with hors d'oeuvres served between the courses. And all the bubbly you can drink. It comes in at about $50 per person but if you are of the school of m-more mimosas (or Bellinis or straight prosecco), you can't beat it. They pour it like the Russian's are marching on Yonkers.
If you want to spend some bucks (big bucks) for a really unique NYC experience, go for drinks at The Campbell Apartment at Grand Central. It will take you way back in time. https://ny.eater.com/2017/5/18/15658014/the-campbell-now-open-grand-central
For breakfast just grab whatever your hotel offers and you can usually find a reasonable coffee shop for lunch. You can always just grab a slice (Manhattan pizza is fine--it's just not really authentic NY pizza--you get that in the outerboroughs) or a hot dog. Perhaps some falafel from a food truck.