I'd say if you want a well defined trail system with some meadows to play in, etc. Its hard to be the Black Hills of SD. Not much for climbing, but there are a few areas to try. If you want some thing more challenging, the Bozeman, Big Sky area of MT is nice too. Lots of climbing and powder meadows. If you want some more challenging area, Cooke City MT offers plenty of deep and steep. Probably not a good choice for a new mountain rider though.
Wherever you go, find a local rider to take you around for at least the first day. You'll be glad you did. Being lost or riding forever to find decent play areas sucks.
Get the right gear. Rent or buy some beacons, probes, and shovels. Never ride alone. Be safe, and have a ton of fun!
Rick