You’ll find Twin Falls in the southern section of Idaho, roughly 100 miles from Craters of the Moon National Monument. While not always as popular as the northern half of the state, south Idaho also has its share of public lands for hiking and camping.
The best camping near Twin Falls is south of the city, with large areas of BLM and USFS land available for dispersed campgrounds. Beyond that, you’ll find City of Rocks National Reserve, which offers developed tent and RV campsites near Almo, ID. If you plan to venture out that way, know that while it’s beautiful, your best bet is to be as self-sufficient as you can. Since Almo is a small, unincorporated community, you may not be able to count on all the amenities you hoped for.