Finding reliable fast WiFi at campgrounds is...well, pretty rare. Most who need reliable connectivity use their own cellular hotspot. Of course, there are some very nice areas for hiking etc. that are outside of good cellular coverage, in which case you're rather out of luck on that front (satellite internet aside).
The general area of the Great Smokey Mountains National Park (Asheville, NC; Pigeon Forge, TN; etc.) might be one area to consider; you've got at least most things on your list not too far away and some very lovely countryside as well.