Maybe you'd be better at this than me, but I've looked at just about every optoin there is off the road system. Cheap and sucessful aren't really in the same catagory unless you know an area awell. You can go on a cheap hunt, but dont' expect to kill anything. I know there are guys that get it done, but they've also spent a lot of time reserching/scouting to find the right spots.
My advice would be to first, pick the animal you most want to hunt, then plan your hunt around that. Between state and Federal land there are endless places to hunt, there are also miles and miles of country with very little game in it.
What do you consider reasonable driving distance?
Renting a car up here isn't cheap... plan $100 a day or more, and there are roads that most rental places won't let you take their cars on (i.e. the Haul Road)
Places where you could have an op at moose and caribou off the road system is slim to none especially, a fly in hunt isn't much better. They tend to live in diffrent areas. Black bears are fairly abundant, but the farther you get away from water/coast/north the fewer you'll see.
There are a few areas that offer 'any' moose, but the odds off the road system is slim/none due to there not being many roads to speak of.
An archery hunt or a pack in hunt off the Haul road north of Faribainks would be an adventure I think. Inside 5 miles either side of the road is archery only, outside of that you can hunt with a rifle. I've not done this hunt yet, but have talked with a lot of guys that have. Success rates vary, due to experience... I think on average it runs about 15-20% with archery and a bit better with a rifle. Its a about a 16 hour hour drive from Anchorage. Renting a car and driving up from here won't be bad. I'd fly into Fairbanks and save yourself half the driving time since you're flying up anyway.
Black bear hunting is another option. There is all sorts of opportunity around Anchorage with in 2-3 hour drive. You can hunt moose as well, but there is lots of competition off the road.
Personally if you're going to spend the money to come up here, save a little more and do a fly in. Start with air taxi services before you look at 'non-guided' fly in hunts. The air taxi will charge you by the hour to fly. A drop hunt with 1 hour fly in and 1 hour out will run you $400-700 per hour depending on plane type/capacity and you could potentially split that.
Going to an area 'cold' and expecting to kill something will be challenging. I've been up here nearly 2 years and am still learning new areas. The one thing that all areas have in common... is the really good looking places are very difficult to get to off the road. Either a river is in the way, its thick azz bush, or a bit farther than I can hike and return with an animal.
Another 'easy' type hunt would be a sitka deer hunt in Kodiak off the road system. It gets pounded by other hunters, but its a 'cheap' hunt. Fly to Kodiak and rent a car...
Good luck on your planning. Spend some time poking around on the Alaska Outdoor Forum. Lots of info there.
