Grumpy, Wyoming is probably your best bet, although you will have a hard time getting a tg over the counter that has alot of public land. If I were you I would apply for one of the better units with lots of public and then put in for unit 47 or 48 type 2 tag for your second choice. These are good units wiht lots of public land, but this is the second season. It can be better than the first because the goats migrate into the units. Montana has some easy draw units that have quite a bit of public as well. I have not hunted there for antelope, but have been there for other game and they have lots of antelope.
New Mexico is cheap to apply for and the tags are reasonable, but the odds suck. A guy should still apply as they assign you to a ranch and have some of the best big antelope hunting
Utah is cheap to apply for as well and some of there units are not too hard to get drawn for. It costs $6 for NM and $5 for UT, so it is a cheap chance and you might get lucky.
Wyoming is still the best deal and you can get extra doe and fawn tags and have alot of fun in big country. If you go after the first weekend you will more than likely be there all by yourself. Good Luck!!!