The minimum cost of accommodation in Valencia is 9-18 EUR. For this money you can rent a bed in a hostel (the cheapest are places in a shared room with 8-12 bunk beds). Another option for cheap accommodation in Valencia is apart-hotels (a night costs from 40 EUR and more, these hotels are designed mainly for family tourists).
In addition, you can rent an apartment from private individuals - then accommodation will cost from 30 EUR per night, and at your disposal will be a whole apartment with a separate kitchen and bathroom.