Wyoming has non-resident general region tags. From talking to friends, its pretty easy to be drawn for deer each year in some regions. For elk, many I've talked to get drawn about every other year they apply in my area of Western WY. Lots of detail I've not mentioned, but there are plenty of out of state tags for antelope, mule deer, and elk in Wyoming if you stay away from the low % draw 'trophy' units. May try Eastman's Journal--they usually have lots of Western state info on units, etc.
$$$--2010 WY-non resident general & limited quota tags costs: elk--$591, Deer-$326, antelope--$286. Youth tags are much cheaper. Reduced price tags are a lot cheaper, but usually female tags only. "Special tags" are about double the price of the general & limited qota tags listed above, but increase your drawing odds significantly.