I've thought about this a number of times. For the lower 48 these are my two best ideas so far:
Wyoming: From a tag standpoint, Wyoming would be hard to beat. You can antelope hunt nearly every year. Elk tags in good units are relatively easy to draw as a resident and if you don't draw you can hunt the general season. The same thing for deer, and a couple of the general regions are pretty descent deer hunting letting you hunt every year. You could trophy hunt those tags then get some antlerless tags to fill the freezer. If a guy can afford some land, I believe landowner tags are available. I understand Wyoming has no personal and no corporate income tax.
Arizona: From a location standpoint I think Northern Arizona around Flagstaff would be hard to beat. You can hit a lot of great hunting country in a one day drive (SW Wyoming, Utah, New Mexico, Southern Nevada, Western Colorado). Very good late rifle elk hunts or good archery elk hunts can be drawn every 4-5 years. OTC archery deer is available. Good landowner tags are available in NM and CO. For fishing, Lake Powell is only a couple hours away and is amazing for stripers, bass and crappie. A guy could keep his freezer chock full of fish. In the winter, the desert is only a couple hours south.
Now if all 50 states could be considered, and you were flexible, I think residency in Alaska, living there in the summer and fall then heading south for the winter would be hard to beat. Salmon and halibut fish in the summer. In the fall hunt sheep, moose, grizzly, black bear, goat, Sitka deer...etc...without a guide or outfitter. Alaska I understand has no personal income tax, no sales tax, and an annual dividend kickback to residents.
