Now you're talking!!!
If you go to the southeast coast in peak summer, try to stay right on the beach for the best breezes and easy access to AC after lunch on the hottest days. This is really for people who are used to east coast humidity or who love the warmth/heat. You may enjoy it more in a year or two.
Atlanta's elevation is only ~1000-1100 ft above sea level.
Temps drop by 9-15 degrees for every 1000 ft you rise (depending on humidity, less change with higher humidity).
Asheville NC's elevation is only in the low 2300's so a visit to this area will only be ~10-15 degrees cooler (and less if you stay within the warm Lake Lure geothermal belt). But the mountain run-off rivers through the whole region and the deeper lakes are still always refreshing and cool. If you want to be relatively near Asheville's sightseeing and you want it a little cooler in peak summer, choose Sapphire Valley or Maggie Valley over Lake Lure (a few degrees warmer in Lake Lure may be more appreciated in spring and fall).
If you don't care about proximity to Asheville and you want it cooler, look to the higher NC mountain towns around the Banner Elk, Boone and Blowing Rock areas, ~3200-3700 ft. This will give you a 20+ degree relief from Atlanta's heat. Pack a lunch to visit Mt. Mitchell at 6884 ft, the highest peak east of the Mississippi, where they can even get freak snow in any month of the year.
Pickens SC has the same elevation as Atlanta but there are lovely, shady, waterfall hikes and some state parks have diving boards on a lake platform so you can dive into deep, cool water. Go tubing in a mountain run-off stream. May be nice for a summer weekend visit too.
If you visit the Gatlinburg/Pigeon Forge/Sevierville area of TN, the tourist areas are very hot in peak summer (similar elevation to Atlanta). But the creeks and rivers through the Great Smoky Mtns Nat'l Park are still cool and refreshing. Shady green roadways and trails throughout the park afford gorgeous mountain views and picnics in much higher elevations too.
BTW, if you're new to this part of the country, you'd probably really enjoy a visit to this area of TN and the GSM Nat'l Park - especially Cades Cove, about 45-60 min drive from Pigeon Forge. Again, the elevation here (inside Cades Cove) is similar to Atlanta, so it may be best done on the coolest day of a week-long summer stay in the area. And on Weds. and Sats. in summertime, it's closed to cars until 10AM, so either bring your bike and be there at sunrise (when it's coolest) on Wed/Sat or choose a different day to be there by about 9AM to beat the midday crowds driving the 11-mile loop. Pack lunch and extra drinks, swimsuit, towel and watershoes or river sandals. Plan to spend the whole day touring historical buildings and sights, picnicking, watching for wildlife, swimming in a lovely stream in Townsend, gawking at the beautiful scenery, maybe riding horseback or in a carriage ride through the woods - all but the last two are free.
Wherever you try, in the mountains of NC, SC, TN or GA, choose a resort with a nice pool and enjoy a lake swim from a rented boat, whitewater rafting, tubing, or waterfall base wading. Trading into the mountains is not as difficult as getting a prime summer beach exchange. And there are plenty of options for enjoying the outdoors without wilting, melting or otherwise sweltering.
Summer weather here in the NC mountains, near Asheville, rarely goes above the upper 80s, and when it does, we usually get a 3PM thundershower that tends to cool things off, rather than making it more steamy.
HTH.
