Staying in Venice itself may not be for the budget traveller, but there are plenty of mainland accommodation options and it’s not too far to travel. Some, like Camping VillageJolly, even have a shuttle bus (which is convenient, although it may work out cheaper to take public transport).
Keep in mind when you visit, however, that Venice is not just a popular tourist attraction (for which reason, you may want to go early if it is going to be nice weather during the high season so you can avoid the crowds) but also a living community. Try to be sensitive to the locals by keeping noise to a limit, using rubbish bins, and if you can, support local businesses.
Venice is littered with picturesque bridges, and there are some incredible churches to visit too. The Basilica Di San Marco is beautiful, among others (many of which do not permit photography, but have beautiful ceiling frescoes that rival those of the Sistine Chapel in my opinion, nevertheless). As always, a donation to the upkeep of these institutions is appreciated, but most do not charge for entry.
The Libreria Acqua Alta is well worth a look. A bookshop that frequently floods, it has books stacked in gondolas and baths. Damaged books have been used to create a mountain in one courtyard and a staircase in another that you can climb.
Food in Venice is of course touristy but there are some affordable options. At Dal Moro’s Fresh Pasta To Go you can get pasta in a box with your choice of sauce. At Fried Land (how could I resist that name?) you can find incredibly delicious seafood, sold in a cone.