Majestic World Lodge in the Allegheny Mts. of Pennsylvania offers good elk hunts for less than $3,000.00. It's a high fence operation but the animals are not tame. They even offer a discounted hunt for "promo bulls" which are an un-intentional cross between European red stag and North American elk.
The Lodge is very comfortable, food and beds most excellent. The hunting is not high exertion but I recommend hunting with an open-sighted lever action carbine or big revolver to make it more challenging. Archers are welcome, too.
Contrast this to a drafty tent and older cot. Snow squalls in the Bighorn Mts. of Wyoming just add to the misery. Plan to spend a whole lot for a 6 day pack-in wilderness hunt and return home feeling exhausted.
I've not hunted at this Lodge but spent an enjoyable weekend relaxing with my wife. We stalked a herd of elk (un-armed). Their fallow deer are equally fun to stalk and photograph.
Jack