I live in Apison. 20 miles east of downtown Chattanooga. Nice, small, growing, unincorporated(lower property taxes), but with all of the benefits of living in Chattanooga. 15 minutes from Hamilton Place mall. 30 minutes from downtown. Closer to the Smoky Mountains and the Ocoee. We take the little ones to Dollywood many times a year.
Good mix of old/new homes and neighborhoods/farms/privacy. I live in a neighborhood with 1.5-5 acre lots that is surrounded by cattle/horse farms. There are also neighborhoods that are more front porch living. Low crime.
You will want to stay in TN with no state income tax. Sales tax would be cheaper in GA, but your commute would be farther, and gas tends to be $0.20/gallon cheaper in TN than the Ringgold area. Ooltewah and Collegedale are nice areas as well, but property tax is almost double.
Not sure where your commute would be daily? That needs to be a consideration as well. Traffic and the never ending road construction on I-24 are terrible for a city the size of Chattanooga. Luckily I do not have to drive into downtown for my job.