Re: what state to elk hunt?
You have gotten a lot of good advice up to this point. I would say because of this being your 1st elk hunt, go on a guided cow hunt. Try to pick an outfitter that will not only sell you a hunt, but one that would teach you a little about elk, and elk hunting. Cow hunts as a rule are much cheaper than bull hunts, and success rates are usually pretty high.
I would look at Wyoming, New Mexico, and Colorado. I have hunted all three of these states plus Oregon and Montana. If you're interested in New Mexico I will tell you I spend May to the Middle of September guiding fly fisherman on a very large ranch in NM, ( Vermejo Park Ranch) it has a cow hunt that has a very high success. I don't guide hunters on the ranch but I know they do a very good job on these hunts, but really if you do your home work you can find good hunts in several different states. If I can help you in any way shoot me an email.
Good luck Gator