When I was a kid in the late 50's, my neighbor went on his first elk hunt. They left the house at first light and was back at 10:00 AM with a whole elk in the back of his pick-up. It seems that on their way to their chosen hunting spot they saw a 6X6 bull standing on the edge of a road bank. They shot it, backed the truck up to the bank and rolled the elk right into the back of his truck. When they got back home, the man said "what is so hard about hunting elk"! He never hunted them again because there was no challenge.
That was in Grants Pass, Oregon. So if you are looking for an easy hunt that's the place to go!
Seriously, just about all of the western states have their pros and cons. It's not an easy question to answer. Read the elk hunting forum here and you will see that elk are available everywhere but drawing a tag is not always easy. I would look for a state near you, that has good numbers and review the Eastmans MRS section of their magazine. Good luck on your quest!