My best friend lived in Rapid City for a number of years. The winters can be rough (they got stuck in a blizzard there in March if I recall correctly) but there is LOTS of game in the area. Also (if this is of interest to you) the fly fishing in the area is just spectacular.
We parked my 4x4 waaaay back off the beaten track one time and hiked down a gully to a really pretty spot, cast to (and, as I recall, caught) a few rainbows and had a general blast. On the way back, we had to maneuver *very* carefully through the trees to my truck because a 1-200 head heard of buffalo decided they wanted to graze by my vehicle.
I wasn't hunting on that trip but we also saw mule deer, antelope and all kinds of cool stuff.