Cheap hotels by international standards are almost impossible to come by in Stavanger. It is a small town which due to it’s petroleum industry, has a lot of business travellers all year around.
This naturally pushes the hotel prices up. You should be aware that unlike most hotels in cities around the world, Stavanger hotels turn the prices DOWN on weekends and in summer, because business travel is less frequent then. For this reason most hotels do have campaigns and special offers in the summer months (late June to early August).
Check with the big hotel chains (most of them are mentioned under Budget Accommodation) if they have any special campaigns going on when you’re planning your trip. If you really want to save money you can rent a very basic cabin or stay in a tent at Mosvangen Camping (more info here), about 20 min walk from the town center. A cabin with 2-3 beds is 480 NOK per night.