Moose - fuhgetaboutit. Bullwinkle will cost you. Now, elk, black bear and mulies - go to Colorado. Haven't hunted there for a few years, but I used to live in Boulder. Killed one 5-point bull there. Not the greatest place for big trophies, but there are lots of elk (go for the draw on a cow tag if you're after meat), good access and lots of public land. When I lived there, deer tags were hard to come by, but last time out, they were in less demand. The economy had hurt business, but it might be coming back now. I should have got one, because while I didn't get a chance at an elk that trip, I encountered two trophy mulies together. I always bought a bear tag. Although I never filled one, we usually saw tracks, and if there are gut piles...
You can DIY there, just get in shape, take chains for all 4 (yes, I used them) and be prepared for weather. I've not done it, but a friend of mine used to rent horses every year. Although I have a tenuous relationship with the equine race, they are invaluable in the mountains.
Not cheap, but another option is to find an outfitter that offers drop camps. Probably half the cost of a guided hunt. Personally, I'm planning on heading to Idaho in 2017. Used to live there, too, and I have friends in Idaho Falls. But tags are more costly, access is more difficult and there are more 4-legged competitors there. Good luck!