As troutslayer mentioned, Montana is a great state to apply for sheep tags. Just make sure you don't apply for the second choice or you could end up getting a ewe tag!
For a non-res, the fee is just shy of $800 but you will get all but about $40 back if you don't draw. The only downside is Montana requires a cashier's check or money order. No credit cards. Also, once you put in, you can only miss two or three years before they will erase your points so you are kind of "locked in" to coming up with around $800 every year until you draw.
If it's not far, it's boring.