There's absolutely nothing wrong with dining on a budget... it's a major money-saver! However, just because you want to save money doesn't mean that you can't sample the best of Valencia's food! Not only is Valencia known for its scrumptious food - fresh produce, seafood, paella, etc. - but it's also known for its extremely wallet-friendly dining options.
Consider hitting up one of Valencia's markets - the Mercado Central is a great suggestion - to grab fresh food for a picnic in the park; it's a fantastic way to economize, eat delicious regional specialties and commune with the great outdoors! If you're not the picnic type or simply want to soak in the atmosphere of a genuine Valencian restaurant, there are ways to do it all without devastating your bank account.

For lunch, seek out restaurants advertising a "menú del día." This means that, from a set menu, you can choose one appetizer and one main course along with bread, a drink and dessert. For as little as €5.00, it's not a bad deal! Dinner time, on the other hand, is the ideal time to check out Valencia's tapas scene. Not only is it a sure-fire way to save money, but it's also a genuinely Spanish way to savor all sorts of local specialties.
Budget restaurants and tapas bars can be found throughout the city, however the areas of the Ayuntamiento, El Carmen and surrounding the train station are chock-full of locales that will leave both your stomach and your bank account happy.
A few budget restaurant suggestions: