Idaho's spring bear goes until June 30, I got mine last year around the 25th. Also could look into muzzleloader hunts for cow elk for the Thanksgiving break.
If you like the idea of sitting water with a bow in 100 degree heat, look at California Blacktail. Rifle Opens in Aug If you are interested in landowner tags you can find some places who will offer November hunts. That is usually an outfitted deal though
There are still some late season deer hunts Thanksgiving in the Idaho Panhandle. Mostly Whitetail but there are some Muleys scattered.