Head to the Dorsoduro area of Venice if you want to save a few euros. It is located on the south side of the city. It has the highest concentration of places where locals, especially students, go to eat. Generally staying away from the main squares will be the cheapest option. If you're willing and able to walk around the town, some back streets offer the best food for the lowest price. Seeing the city from this vantage point is a lot of fun too!