The vast bulk of travelers to Utila come for the diving, and end up staying in a dive-shop affiliated hostel. This is by far the cheapest, most sociable option, and the quality of accommodations should play a major part in your choice of dive shop. You can stay as a non-diver at most of these places, but you'll find the prices relatively expensive (around $8-$10 for dorms).
As a result of this tendency however, there are relatively few unaffiliated hotels on the island (and no unaffiliated hostels). The majority of independent lodging caters to a more upscale crowd, such as the glamorous villas for rent down past Bayou beach.