Most definitely, you can pretty much camp anywhere within the walking distance to the petroglyphs. There are also endless lands if you want to be further away from the main area, secluded. It's a high desert area, also very nice for stargazing.

There are tons of places to camp in the area. I preferred camping down Jackrabbit Rd where there was little traffic. And yes, the weather is nearly identical to Cedar City. They are only about 30 miles apart.