Download hunting maps from onx, you'll have all public land of all sorts along with land owner information on your phone. For $100 you get an SD card you can load on your gps. I kept it on my tablet for driving around and the gps for hiking.
Most landowners don't care about goats. There are a billion of them and I general a pain in the [beeep]. But they do care about their cows and anything that will cost them. Still expect to pay a tresspass fee and be a good guy and drop off the landowner tag when youre done. The state pays them a few bucks for each tag. But odds are you'll find something on public land. If you have a young kid hunting, especially his first hunt don't be surprised if you not only get access but a ride in the ranchers truck straight to where he knows goats hang out.
I had free access to a lot of land, ranchor usually charged 700 a gun. At the beginning of the season I'd call them up and let them know what I was driving that year. 10 seconds after you cross a fence the rancher starts getting phone calls from other ranchers that you never see. I still hit public unless I saw something good on his ranch and would stop by after to be for a bit.
For $4 you can get a paper map from blm, but they haven't updated in years. A lot of what the maps show aren't accessible anymore.