I have lived in Washington, Wyoming, Montana, Arizona, New Mexico, California, Maine, Florida, Hawaii and in 5 other countries thanks to my Uncle Sam. Grew up in Wyoming and currently live in New Mexico.
Here is my take on this controversial topic.
Nobody wants you to move to their honey hole. So the odds of getting an honest answer are completely off. I personally don't care where you move.
Here is my 2 cents:
Wyoming. There is decent over the counter hunting, but it will be competitive. You can hunt elk and deer every year over the counter. Fishing is pretty good, and not super crowded. There is no resident points programs for antelope, elk and deer. You may spend 3-5 years between buck antelope tags.
Montana. Also has decent over the counter hunting, because most of the state is OTC. They were stupid and adopted a resident points program. The goat, moose, bison and sheep tags are on a bonus points program, so you could possibly see one or two of those tags in your life.
Idaho. Has decent over the counter hunting, if you are a bowhunter most of the elk and deer tags are OTC. No points program for anything. More people than Wyoming and Montana, and less land. It would suck to live in East Idaho or Boise and not be Mormon and be single.
Arizona. Great quality hunting if you can draw a tag. Preference points program you are 30 years behind on. Fishing is ok, desert state. Scottsdale looks like a good place to be single, tons of fake boobs.
New Mexico. Great quality hunting if you can draw a tag, but no points programs. We have been residents for 3 years and I have drawn; elk, a crap deer tag, a great deer tag and a javelina tag in that time. If you bow hunt you can almost always draw a tag of some sort. Close to Arizona and Texas for draw hunts. Fishing is better than Arizona. Mostly desert state. If I was single, I am not so sure I wouldn't stay here, as it there are tons of hot women as long as you like spicy Latina brunettes. Especially down here near El Paso.
Alaska. I was single in Alaska the first time, yep. It is a boring place to be single. There are so many single dudes, that a lot of the women are tired of being chased and have given up on men. I was single in Barrow as well as Sitka. In Sikta it sucked, in Barrow it was fine. But I was 25 and all the women were in their mid 30's. They still dated me, but there wasn't good age matches.
There are also a huge number of wallet and chain lesbians in Alaska. So that doesn't help your odds. Fishing in Alaska is the best it can be. Hunting is based on your ability to get to it, because you bought the equipment or paid someone to take you out there. The draw hunts in Alaska have really poor odds. Bear hunting for grizz is over the counter and you can shoot 2 a year. You could hunt dall sheep, mountain goats, moose, grizzly, wolves, wolverine and more every year OTC. Kind of hard to beat that. And have a trap line. Especially if you lived someplace like Glennallen, Tok or Cantwell on the road system. You would still have internet connectivity for your job.
Utah, if you are single and not LDS I wouldn't consider moving there. They also have a super lopsided points program and you'll never get a tag. Quality of hunting is superb.
Nevada. Good place to be single. Points program has been developed for 20 years. Quality of hunting if you get a tag is very good.
Washington and Oregon. Ok place to be single if you like hippy chicks or want to date a transgendered dude. Hunting is a train wreck with long screwed up points programs.
Hooved animal Hunting quality ranked: New Mexico, Arizona, Utah, Wyoming, Montana, Idaho, Alaska.
Bear hunting and trapping ranked: Alaska. No place else is even close.
Hunting tag availability ranked (provided you can get to it): Alaska is so far above anywhere else, then Wyoming, Idaho and Montana. I put Idaho above Montana because of Montanas stupid points programs.
Single opportunity ranked: Arizona, New Mexico, gets really weird after that. Depending on how old you are there will always be single moms, and very few professional single women that have never been married. The Northern Rockies is going to be tougher than the Southern Rockies for dating.
Cost of living ranked (cheapest): New Mexico, Montana, Alaska, Idaho, Wyoming, Arizona in that order. ID, WY, and MT have housing booms that haven't even started to fall at all. Alaska and New Mexico had a mild housing boom. Western Montana is more expensive than eastern Montana.