You can choose from several states. Wyoming and Montana have alot of prairie goats to choose from. New Mexico seems to have the bigger heads if horn size isof importanceto you.
I've only hunted Montana for them and found the state to be well populated by antelope. You can book a three day or one week trip. If a quality goat is your goal, make sure you try to get the first week of antelope rifle season on your tag. They get real spooky as the weeks roll on and guys keep shooting at them.
If you're ok with shooting far, any week will work, but the best heads have been culled already. Lots of folks out west seem to stop the truck, grab their rifle and shoot at the antelope they see in the prairies. Makes 'em real spooky. Early season is your best bet for making choices and lots of stalks.
I used a .270 and shot mine at 310 yards after crawling on my belly for 75 yards! I was on a combo hunt(deer & antelope) so I was there later in the season(Oct).
Practice your shooting from prone with a bipod and sitting with a pod. It'll help you when the long shot comes.
Good luck!