Cactus Forest!
Free. Wide open space, an abandoned air strip. Really cool cactus variations all around, you can hear coyotes. And there are wild burros in the area you can def hear them and during the week it's likely you will see them! It is popular for ATVs and such, so it can get a bit noisy, and it apparently gets pretty packed over the weekend. But empty during the week. About 30 minutes away from town. Though there are a few paid campsites in the area. Not sure what the stay limit is, probably 14 days. All the cacti so close is a bit hazardous for pets and small children, my dog already got spines in her paws.