I would start looking at states that have over the counter tags, as getting a tag might be harder to do, than just finding a place closest to you might be!
and are you wanting to do a self guided hunt, or hire someone to take you hunting for things?
might be worth emailing some outfitters where tags are over the counter and asking if they do Cow hunts, as many ranches do try to control numbers this way and make a few bucks at the same time, but will get you on more prime land, with higher odds of filling tags,
unless again you wish to do the whole hunt yourself, then?? and if planning to do hunt yourself, are you sure you have all needed gear and skills and physical conditioning to get a downed elk out!