The southern end and out towards the badlands if you want mulies. The closer you get to the Black Hills the better chance you'll run into whitetails. I'd stick with the BLM country out in the Badlands. But don't forget you have to draw the tag.
Non-resident archery tags are "unlimited" - meaning you have to get them through the mail or internet - no preference points needed for archery. South Dakota has a great website that shows all public land in the state including BLM, walk-in, etc. go to http://www.sdgfp.info/Wildlife/PublicLands/PubLand.htm - that should hook you up for all public lands in the state. IMO for bow hunting i would think the grasslands south of Hot Springs would be a good spot to go to, or the BLM and walk-in area up in Harding Co (north of Rapid City)
Jim Zumbo, Craig Boddington, Ron Spomer and Wayne Van Zwoll are all solid contributers to the modern hunting literature. Through their gifts (both hunting and writing) they make us better hunters. Whether it is letting us learn from their mistakes or by teaching us new techniques,they help us harvest more game. But I suggest looking to the oldies, the fathers of the outdoor writing craft, to learn tricks that you might have not used.
I chose to shoot the 270 winchester because I grew up...