Here's a list of the best places to eat in Israel. In the vast majority of them you can have a good meal for 20NIS or under, they have local reputation which goes back decades and hardly any tourists buy from them because they require local knowledge. Most of them don't have any signs in English so you would need to ask around. It's enough that you say the name written here and people will show you where it is.
Hummus Sa'eed in the market (Best hummus in Israel, songs have been written about it)
Falafel Orion (Hertzelia St)
Falafel Armon (Haneviim St)
Haloon (Shabtai Levi St)
Pninat Ha'ir (Jaffa Rd)
Falafel Hazkenim ("Elders" falafel, Wadi Nisnas)
Falafel Hawadi-Mishel (Wadi Nisnas)
Shawarma Sabach Borthers (Alenbi St, baguettes are recommended)
Tel-Hanan Ice Cream
Falafel Neto (Iben Gabirol St)
Hummus Asli (Ben Yehuda-Dizengof Intersection)
Hummus Abu-Hasan (Ali Karwan) (Yehuda Hayamit St)
Shawarma A-ouni (Yefet St or Hamasger St, baguettes are recommended)
Abu-Lafya (Yefet St and also Hayarkon St)
Sandwich Rami (Bugrashov St)
Hummus Pinati (city centre, really famous)
Bagdadi Hummus (Old city Muslim quarter)
There are many more but I don't know Jerusalem well enough.
After you eat in all those places you would probably never want to go back home.