You need to decide what you want to hunt. Unfortunately you can rule out Nevada unless you have lots of money to buy a landowner tag. the deer and elk is by draw and without bonus points you won't draw. I am not sure on the residency requirements either as to needed to be guided.
Here are some ideas but it would help if you gave some parameters to your hunt: How much do you want to spend USD, what species, what method (archery, rifle), how successful-do you want to harvest an animal or the experience? trophy quality?
As with most things the amount of $$ spent will increase the chance of success and trophy quality.
I don't think you would have any problem flying with a bow. A rifle may cause more hassel and its easy to borrow one here and shoot. I couldn't imagine borrowing a bow though. there are a lot of guns here.
here are a couple ideas-
I think the best hunt in the US is an archery bull elk in the rut. You get to see the higher elk country and get the bull experience. At this point Colorado is you best bet with the season Aug 25-Sep 23. However OTC DIY success rates are very low- 15%. to be successful you would definately need a local or pay a guide. You could shoot a cow elk if you just the experience. A guide can cost from $1000 to $10,000 depending on location and trophy expectation and tag availability.
Whitetail deer the most hunted animal, but you would have to go to another region, and the best hunts are in Nov. archery season does start in mid sep-oct1 in various states. You will need private land to be successful at this point and stands set. some is done by High Fence and bait. I think you could find hunts for $1000-$4000. Not as scenic or the experience of elk, but can be excititing.
Mule Deer- like elk and maybe a better chance to harvest but a true trophy mule deer is hard to come by. there aren't many OTC mule deer tags anymore, would have to look north to Idaho, CA does have a lot of blacktail and you could get on a good ranch there, there are hunts, archery and rifle in that time frame too. You could buy a landowner voucher in CO for that time frame too. should cost from $1000- $4000.
Antelope- I think this is the best option! Often over looked and underappreciated. The archery hunts are in Aug-Sep and rifle are end of sep-Oct. High success rate hunt and affordable. western area hunts that you may be able to drive to. there are OTC archery tags in CO, WY may have leftovers. should find a good hunt for $1000-$2500.
also make sure you have a hunter education card.
Good news is that there are usually pretty inexpensive air fares to and from Las Vegas to other parts of the country if you end up adding a flight.
A week in a mountain town in Colorado with a rental car might be a good option. The ski towns have plenty of nice lodging/cabins for rent, good shopping and restaurants, and you can easily stay in town and either drive 1/2 hour or 45 min to hunt elk on public land (National Forest Service & BLM) or have the wife drop you off and pick you up at dark or when you call.