I'd worry less about the distance from Virginia (you're probably planning on driving) and concentrate on the areas where you're most likely to draw a tag. Depending on how soon you want to do this you'll be presented with a great number of choices of State, GMU, time of year, etc. Costs of the trip are also a big factor, of course.
If you're patient and you really want a special hunt, you may want to apply for one of the limited access areas offered by several western States. You won't draw a tag for a while but will collect preference points which will eventually lead to a tag. This isn't the best solution for the eager hunter but its a strategy which is most likely to bring success when you do finally get to go there.
I have a friend who applied to hunt a very limited area in New Mexico for years and finally drew a tag. The result was a massive 6x6 bull. The rack doesn't fit in any room in his home so it sits out on the back porch.
Finally, cow tags are usually easy and far less expensive.