Alaska would be nice. But I'm also a realist. A brown bear hunt is $20,000-$30,000. Sheep and goats are probably the same or more. Most everything else can be hunted closer and cheaper. A summer fishing trip is financially more likely for me.
For me, my ideal hunting trip would be a guided back country elk hunt. It would still be a once in a lifetime thing, but possible. A DIY hunt for elk is very doable, and will be my next trip.