I would go to Tennessee and visit Pappy. In fact I am going to try to next year. He is a great guy and I am sure he would hook you up with an opportunity to shoot some arrows.
The hunting is great in the West US. To us a 200" mule deer is a very nice deer, but not huge. Trophy elk are 370" and bigger. It is however a lot harder to get a tag and you would be limited to shooting one deer, elk pronghorn, mountain lion etc. If you go to the Eastern States you have potential to shoot a buck and a doe the same day and more the next day, depending on where you go. If you decide you want to hunt in the Utah, Nevada or Arizona you can shoot some huge stuff, but you have to put in for a drawing and it will probably take a few years to draw a tag. If you decide to go that way, and get a tag, I would be happy to scout the area and find the game before you come.
For a special trip like yours I would go East where the numbers are higher and opportunity to shoot more game is good, even if you donate the meat to a shelter.