Now offering FREE High-Speed Internet Access in ALL rooms. The La Quinta Inn-Fort Stockton is located along the northern edge of the Chihuahuan Desert, not far from the banks of Comanche Creek. Visit Annie Riggs Memorial Museum and the museum at Historic Fort Stockton. You can walk to the golf course and to a variety of restaurants. Fort Stockton has parks, a civic center, coliseum, the Historic District with 16 points of interest and a municipal airport.