Don't apply for a tag completely on the assumption that you will be able to hunt the "Walk in areas". What I mean is; the landowner that has leased that land to the Wyoming Game and Fish can decide to pull the land out of the lease at any time. This happened last year near where I own some property. There were quite a few hunters that got to Wyoming and found out that the area was no longer a "public walk in area" and had to find other places to hunt in the area they had tags for. This probably only very rarely happens, but it sure would suck if it happend to you.
If you want to hunt public land, then your best bet is to try and locate an area that has large parcels of public land (3 or more Square Mile Sections joining each other) that has access via a county, state, or US roadway. Even in North Eastern Wyoming, where I live, there are alot of these "blocked together" public land areas. Then, once you get a tag and arrive to hunt; you can always go try the walk in areas too.
If I were a nonresident coming to wyoming to hunt Antelope.......I would not even consider making the trip just to "Road Hunt". What I mean is; some folks will come out and drive the county roads looking for game. When they spot game, they'll try to determine if the land is public or not. If it's private land, they will sometimes try to contact the land owner to get permission. Sometimes they will just try to hurry and get the game down and loaded up before a landowner catches them.
As a landowner who allows only X number of animals to be taken per year, and is usually "booked up" at least 6 months in advance, this is very irritating to say the least! I do post and patrol my property so the hunters that have gained permission don't have to worry about the poachers/road hunters, and they can enjoy their time hunting the way hunting should be. But landowners here are not required to post their property, so alot of them don't.
On another note; small (1/2 or 1/4 section) parcels of public land are sometimes tempting to try and hunt, But these are usually surrounded by private land, thus being "land locked".......ie, no public access. Antelope cover a huge amount of acreage, and rarely stay in such small parcels.
There are usually no fences around these areas, because landowners have leased these lands from the government for many many years. I would like nothing better than to swap these little areas and have them moved to places where there are bigger blocks of public land. But our Government is moving like molassis on that one.