Free: Contests & Raffles.
Look at the previous year's likelihood of draw. Some areas with large bucks are 2-3 years wait. Most areas that have left over tags or a big possibility for a 1 year (first year) draw are mostly private land or landlocked public (same thing). If you want to pay to hunt (a guide) eastern Wyoming is great, from Gillette to Casper. There is good hunting everywhere in the state, it just depends on what you are really looking for.
Saratoga, WY was loaded with antelope a few years back. Saw well over a hundred per day. Haven't been there since '01.