Many libraries offer low cost library cards for non-residents. Check all the library branches in your state, as some offer library cards to non-residents who still live in the state for free.
If you want a larger catalog to work with, major city public libraries, such as New York City, Philadelphia, Houston, Los Angeles, and Boston provide the best variety to make the fee worth it.
Some states such as Texas's TexShare card, offer cards that allow patrons that are in good standing to access other libraries in the state and check out a limited amount of books at different branches.