Don't underestimate state parks. I frequently use them when time is limited or weather is iffy. One big advantage is that they're close: if I'm leaving on Saturday morning and need to be home by noon Sunday, going to a state park that's half an hour away maximizes my time on the trail and eliminates the "gotta make miles" mentality from my driving. It's also cheap (minimal travel expense) and doesn't take any elaborate advanced planning.

I frequently use a local state park in the winter, for a couple of reasons. First, all the summer crowds are gone and I've got the place to myself. I usually circumnavigate the lake (a mixture of trail and off-trail hiking, which keeps my compass skills somewhat current) - about 12 miles of rolling terrain. The beach that is wall to wall people in July is wall to wall Canada geese in January, and I've seen 8 or 10 deer fairly close that would have been spooked off by summer hikers. Yes, crossing roads and picnic areas can be a little un-wilderness-like - but since they're vacant, it still feels an awful lot like backpacking.

Second, it lets me "play" with gear. I have to camp in the public campground. (Well, I'm supposed to; however, one ranger - I was his Scoutmaster - takes a somewhat generous interpretation of the rules if someone is using low-impact technique.) Since there's no one else in that campground and the bathrooms are locked, I might as well be camped in the middle of nowhere. I usually am, in fact, camped by the car, but I pretend like it's not there - unless the gear I'm testing fails, then I go get the alternate from the car. (For example, if I'm trying to see how warm my sleeping quilt is and find out the answer is "not warm enough," I can go pull my full-out winter sleeping bag from the car.)

Third, it lets me bail in the case of unexpected bad weather. If it starts sleeting, I can simply go home. That avoids issues of hypothermia potential, tent failures, etc. - all the kind of things that you won't want to deal with when you're just getting started (or maybe even ever, when your goal is to get away and relax for a day or two.)

You can accomplish something similar at state parks during busy seasons by getting a camp on the fringe of the campground, and hiking the less-frequented trails. Some state parks (like one I frequent) even have a backpackers' camp that's located a couple of miles away from everything and accessible only by trail.

Using state parks for an overnight may not be "backpacking" in the purist sense, but I contend that if you get out of your car, put on your pack, and live out of that pack until it's time to get back in the car until it's time to go home, it qualifies. And, in a broader sense, if it gets you away and gives you the recharging you need, it definitely qualifies.

I don't know what part of Georgia you're in, but from what I've seen of northern Georgia (my daughter and her family live near Kennesaw Mountain), there are some really nice parks there. Go enjoy them.