Many hotels in countries other than the US, and all B& B's include breakfast as part of the room price. Take full advantage of this and fill up so you won't have to buy food until lunch (or depending on your personal metabolism, dinner).
Eat where the locals do. Casual restaurants with a large local clientele are like to be high quality and low cost.
Eat in ethnic neighborhoods (this tip works in the US or abroad). You can get some first class feasts for very little money in ethnic neighborhoods. Using my hometown of Los Angeles as an example, travel to Korea Town, China Town, Little Tokyo, Thai Town, or in nearby Orange County, Little Saigon for incredible food at coffee shop prices. Do I detect an Asian theme here? Don't worry, there are Mexican neighborhoods all over the City of Angels serving dirt-cheap but delicious authentic South-of-the-Border cuisine. There are also plenty of Ethiopian, Cuban, Argentinean and Moroccan eateries along with just about every other ethnic group under the sun. That's one of the things about living in a large city that's so wonderful. Take advantage of the ethnic neighborhoods in whatever cities you visit for great food at bargain prices.