You can buy a Necklace Fan and sit on the porch at TE with a nice cold drink .
Or bring a lawn chair behind loop 300 and sit under the trees by the lake with a Necklace Fan and a good book,
This isn't AT FW, but if I wanted to read for an extended time in the a/c I'd take the boat to Wilderness Lodge and hang out in the lobby there. That was my plan if it had rained any longer when we were tent camping at FW in 2010.
There really isn't anything inside with AC that would be quiet enough to read. For quietness on the outside if theres a breeze you might try the Trailside Porch or the porch behind the Meadows Trading Post or down by Clementines Beach under the trees if there isnt a function going on. Good Luck
This isn't AT FW, but if I wanted to read for an extended time in the a/c I'd take the boat to Wilderness Lodge and hang out in the lobby there. That was my plan if it had rained any longer when we were tent camping at FW in 2010.