My experience is all in the Casper area. The BLM land west and southwest of Casper is a good start, I think. Inside of 15 minutes from town you can be on goats. I highly agree with everyone who encouraged doe/fawn tags. If you are going to try to get a leftover you are going to need to be Johnny on the spot when they go on sale online. Any tags left after the first dale of leftover sales is available for a reason. Oh and DO NOT hire an outfitter or pay for access. Antelope are plenty easy to hunt DIY for even the most inexperienced hunter. I've only known one person who ate a tag, and that was because he basically chose to.

PM if you want unit/area specific recommendations.