A little pricey but look for discount coupons. Very family oriented and lots to do witht he kids. You really can take some food and drinks in but just not in a big cooler. Take the small lunchbox kind. The river is cold so be prepared.
Most cities have public parks.
Take a picinic and a frisbee or a ball. Next to Atlanta Botanical Garden. Pack a lunch or snack and people watch while you rest. Moderate entry fees. Great to split time between the Garden and Piedmont Park next door.