First off, CONGRATS! Second, apologies in advance for being long winded. It's been a while since I've been up in that area, but we're planning a camping/wheeling trip in the spring in the Smokies to get reacquainted with the area and then try the Georgia Traverse on the way home if time permits.
If you look over a map of the park, there are lots of hikes and natural attractions to fill in the time. That's what I'd recommend as a starting point. Mostly just depends on how bad you want to avoid crowds as to what you pick and how much time you feel like spending in town. There's also likely residual nature area and town damage from the wildfires a couple of years ago, so that may limit some of your options as well.
From what I recall, most of the "off-roading" in the park is a few paved loops (Cade's Cove and Roaring Fork come to mind) and fairly short one-way scenic drives (Parson's Branch in mind here, but that MAY be closed, so check the MVU maps or check at one of the Visitor Centers). Most of the unpaved stuff appears to be in and around Cherokee NF. Regardless, some pretty areas with history exhibits and such inside the park proper. IIRC, there's also some really nice picnic/day use areas around Fontana Lake and the dam.
I've got one trail route that I found a few months ago called Cherohola Loop #1 and #2 that I was planning to try while we are up there. It looks like a mix of Forest Service roads and pavement with part of it covering the Dragon's Tail in NC. From what I've been able to find, it was originally mapped as a sport bike route, so 4x4 should be doable. Maybe someone familiar with the area will chime in and give us both some info. Anyway, here's what I've got saved. If you've got a Gaia GPS account, open it and the USFS 2016 layer should be loaded as default, then add the USFS MVU map and Gaia road map layers to get the rest of the detail.
https://www.gaiagps.com/datasummary/route/d8650356d0d11baa961b77d1d4dba88e46666107/
Have a safe trip and enjoy!
