Wyoming is probably your best option. Take a few minutes to look over the draw results from previous years and find a unit that is possible to draw with no points. There is a second draw this year for the tags leftover from the first draw so trying to buy them OTC is not the best idea.

https://wgfd.wyo.gov/Hunting/Drawing...6-Drawing-Odds

Most of the easily drawn units will have difficult public access, so look for units with legal access to BLM land, walk-in areas, or state lands. In the no-points-required units the public land will have quite a few hunters but there are a lot of pronghorns. You might want to consider a doe/fawn tag or two also. A doe/fawn tag costs only $48 each for a nonresident and can often be had in addition to a buck tag.