wildwilderness
WKR
AZ deer in Dec (draw) Jan (otc with caps) or even better go to Sonora MX- Love bowhunting coues deer in Jan/Feb and mule deer if you can afford it. Of Course Desert Bighorn sheep is Dec-Mar but can't do that every year 
Lots of Nov-Jan elk hunts, Rifle Cow permits are easy to get and can DIY public land pretty straightforward or pay a small trespass fee for many private land options.
Archery pronghorn opens mid August (15th) and is very doable sitting water holes.
California has Coastal zone Columbia Blacktails archery opening end of July-August
Alaska has many summer options for caribou, sitka blacktail, bears, sheep, moose etc. Though summer may not be the ideal time for some of those.
Bison on private ranches or Reservations can be hunted year round (very hard to draw a wild free range tag)
Mt. Lion is best in winter and many states/provinces to consider

Lots of Nov-Jan elk hunts, Rifle Cow permits are easy to get and can DIY public land pretty straightforward or pay a small trespass fee for many private land options.
Archery pronghorn opens mid August (15th) and is very doable sitting water holes.
California has Coastal zone Columbia Blacktails archery opening end of July-August
Alaska has many summer options for caribou, sitka blacktail, bears, sheep, moose etc. Though summer may not be the ideal time for some of those.
Bison on private ranches or Reservations can be hunted year round (very hard to draw a wild free range tag)
Mt. Lion is best in winter and many states/provinces to consider