Alaska would be fantastic but prepare for a serious price tag. Last I heard, the going rate for a guided moose hunt was north of $12K.
Speaking of moose, supposedly the best place (best chances and price) is Newfoundland. Their moose are smaller and don't have big racks but there are lots of them and hunts are much more affordable.
If you want a "Southern" experience, try one of the south GA quail plantations. They treat you like a king.