If one was to move to Alaska, what part of the state offers the greatest hunting opportunities without the need for an airplane ride to access it, or doesn't that exist?
Strictly within those requirements... anywhere within the road system.
If you are talking "local", then the story changes. Currently a resident in Homer can drive to the Brooks and hunt sheep every year, although it would be a nicer drive from FBKS. There are registration (no drawing) goat tags on the road system. Grizz tags are free, and not even needed in some areas.
There is a book published by Fish and Game that goes into significant detail on what you can hunt where, when and how.
http://www.adfg.alaska.gov/static-f...BC0B38917791C11/regulations_complete.pdf