With no points and wanting something next year you should be looking at Wyoming. I had no problem getting tags in areas that are less popular, don't hold as great a trophy potential and are harder to navigate public land. Buck tags are harder to draw, doe tags are easier and more plentiful.
WY's website is pretty easy to navigate, get the information and start going through units looking at the numbers of tags, applicants and point averages for draws. Also, if you aren't fluent with On X maps, you could buy that now and use it in your search, the online version comes for free with the web app and you can easily look at a particular unit and see how much public is there and how accessible it is.
Antelope hunting is pretty much the opposite of most big game hunting, at least the ones I have been on. With most big game, 90% of the effort is finding the animals. With antelope, they are easy to find, 90% of the effort is getting close enough for a shot. The terrain is usually wide open and they have incredible eyesight and don't like people anywhere near them. When spooked, they can move huge distances quickly.
It's a great hunt, very doable DIY or you could hire a guide or access to private land. WY publishes landowner lists and you could call around and pay for access.
Many options for whatever type of hunt you want.
