I wouldn't go to the US... I'd go to Northern BC, the Spatsizi country to be more specific.
Otherwise, I'm quite content with Montana.
I read the OP's query as being where in the western USA each person might like to go, if time, money and all that were not issues. I see, though, that some posters have included certain Canadian jurisdictions as areas that they would choose and, so, I decided to post my choice.
I am quite familiar with northern BC and "The Spatsizi" would not be my first choice, for various reasons. There are other areas of BC that I would choose, for several reasons.
My first choice in Canada, would be probably the Canadian Yukon Territory with one of the top outfitters there, as due to certain political reasons, a Canadian cannot hunt there without being "guided".
My next choice, would be the MacKenzie Mountains of the Canadian N.W.T. and hunting as above.
I have no interest in hunting in foreign countries, but, have close relatives in Australia and would perhaps enjoy hunting there, while visiting, as I may do in a couple of years.
My all-time favourite is still hunting the Kootenays, just returned a few days ago, hot as hades, and NOW the snow is falling.......!@@#%%^^!@@%!!!!!
May get into central BC nexr month for Mulies, but, wish we had been able to go one week earlier for this most recent trip.