My favorite dollar pizza is the one on 9th between 50th and 51st street. Another +1 for Los Tacos #1, Totto Ramen, and Empanada Mama. While I haven't been, I've heard Thong Lor has a pretty decent lunch special for $10 as does Zoralie. Gossip has a happy hour from noon to 10pm on weekdays (and maybe weekends too?), and while they do serve food there I don't remember if any food is discounted for happy hour. Rudy's is another bar that has fairly cheap (for NYC) beers but you can also get a free hot dog with every drink (they're pretty basic and nothing you couldn't make yourself but I guess it's the value that counts, also they're cash only).
It could also be worth looking into the Too Good to Go app, as basically different restaurants will give out "leftover bags" for around $4-6 and you can get a good meal out of that. They do have different pickup times though, so it'll depend on your schedule, and the results can be a bit hit or miss, but you're supposed to get enough food to be valued at 3x what you paid. Amish Market in particular lets you take a pound of food from their hot bar, and Sal's Pizza gives you 3-4 slices.