Have you been to Atlanta? It doesn't seem like you're familiar.
The Beltline [0,1], a paved multi-use trail converted from old railway, encircles the city's major neighborhoods and connects everything. It's one of the city's major features. Dozens of parks, including some of the largest -- Piedmont [2], Old Forth Ward, Grant Park, and the old Bellwood Quarry [3] where they filmed Walking Dead, It, etc. -- are all immediately accessible.
The Beltine is being connected to the Silver Comet Trail [4,5], which is a paved bike trail stretching all the way to Alabama (the nation's second longest). Light rail is also being added to the Beltline.
Outside the city you've got access to the Chattahoochee River for rafting. The Palisades [6] provide excellent river-adjacent hiking.
Stone Mountain [7], a giant granite mountain, is 30 minutes east of the city and provides excellent hiking and running.
Kennesaw Mountain [8] is 30 minutes northwest of the city and is great for hiking and dog walking.
Red Top Mountain is 40 minutes northwest, and you have a host of lower Appalachian mountains to the north.
Allatoona Lake [9] is 40 minutes northwest, where they filmed Ozark, and provides excellent boating. Lake Lanier is an hour away and is even bigger.
Atlanta isn't called "city in the forest" for nothing. We have so many trees, parks, and outdoor activities.
[1] https://en.wikipedia.org/wiki/BeltLine
[2] https://en.wikipedia.org/wiki/Piedmont_Park
[3] https://en.wikipedia.org/wiki/Westside_Reservoir_Park
[4] https://www.silvercometga.com/
[5] https://en.wikipedia.org/wiki/Silver_Comet_Trail
[6] https://www.atlantatrails.com/hiking-trails/hiking-east-pali...
[7] https://en.wikipedia.org/wiki/Stone_Mountain