At this late date, you'd have to find a state that has either over-the-counter tags or a late drawing. I know here in Wyoming the non-resident application period ended March 15th. In fact that drawing's results will be posted this coming Monday.
However, there is a late drawing starting on July 7th for leftover tags. Best bet is to go to http://gf.state.wy.us/downloads/pdf/09Apps/09NRIAEDAInfo.pdfand the G&F home site and research the regs.
Most of Wyoming is public land. BLM, National Forrest, State held land, etc. There are also many private properties you can hunt called "Walk-In" areas listed on the G&F site. That link is called "public access".
Unless you apply, draw, and then know where you can hunt, I'd have little to add as to the deer hunting there. Mulies are all over the state. And some big'uns too!!