While not necessarily cheap, some of the City Walk restaurants have some lunch specials. Seasonally, Emeril's has their "Big Easy Lunch Crunch" that includes an Appetizer, Entree, and Desert for $22. Emeril's also has 1 free Appetizer or Desert per table with an Entree purchase and park ticket.
Also, the table service restaurants in the park are often only $1-$2 more expensive than the counter service restaurants. In fact, the prices at the Leaky Cauldron are almost the same as Finnegan's. So, for the vacation as a whole, a "budget" tip may be to save your table service dining for Universal instead of Disney.