Just North of Redrock Canyon is Opal Mountain, the nearest high point. It is accessable by a crude road and is excellent on dark nights for Astronomy. Other highlights of this area include numerous 4WD trails to the West East and North. (I do them w/2WD). There are old mines to explore (Ext Dangerous) to the East. Especially dramatic is the Old Dutch Cleanser Mine (see USGS topo maps)(very dangerous). The BLM areas to the East of RRC St Park is a fun area for opal and gem hunting. The badlands there are rich with fossil bone fragments of prehistoric mammals. (Just leave them for others to see, they're not valuable and will just rot in your collection.) If you get to know the area there are also many primitive roadside campsites outside the State Park that are good. Red Rock Canyon and the general area is a rich recreational resource. Use it, treasure it, and go low impact. Please plan to clean up trash if you go into the back road areas. It was abused before it was protected.
Here is a link for more on the Natural History: http://members.aol.com/Waucoba7/redrock/redrockfossils.html