There are no backcountry roads in Alaska... seriously. You can hunt off the highway, or from an ATV in a few places if you're a NR. The easier to access areas are archery only or draw. I would suggest you spend some time on the F&G website looking at opportunities for NR and go from there. Alaska isn't like any western state, though can be similar depending on your level of logistics ability. Tags for the new year go on sale July 1, and are OTC at any time.
You really only have 3 options. Fly out of Kotz to hunt the WAC, fly out of one of the eastern interior towns (Fairbanks, off the Haul Road, etc) and hunt the Porcupine or Central herd, fly out of Tok/FAI and hunt the 40 Mile... Or walk in off the haul road which is cheapest, but also has very low success. The priors are all good hunts but will cost you $3-5pp plus travel to/from AK.
Good luck!