I'd say go for a ride to URE and hit Arrowhead probably very quiet this time of year and hot showers etc.. Plus a power post so you could bring a small 120v heater
There is a small field on the right just as you reach the campground, a few signs say no camping there but the dogs would have a ton of room to run.
Something else that is nice is Oak Hollow Campground in High Point. Right on the lake, maybe 3 miles from the mall, so you can run out and see a movie or whatever.
But for getting away from it all, URE...(Arrowhead is closed I think, but the horse sites might be open?)
...or if there is an OPEN invite, DPG, gives ya something to watch too, and I think several of the guys camp overnight during open invites (NOT OPEN ANY OTHER TIME..just had to say it)
There is a real nice campground on High Rock just south on the main drag in Lexington, will be on left before you cross the lake.
I went backpacking in Uwharrie last weekend. Didn't see too many people and it was very nice out there. I always recommend there. Heck, if you head out there lemme know I'm always down for a trip there.
All three of these are an easy drive from the Triad. In fact, I'm planning a camping trip to Stone Mt this weekend. Just hoping that it is warmer on Friday, and dryer on Sunday.
I love Uwharrie because I've always been more into true primitive camping with no facilities. Linville Gorge is an awesome place to go because it's designated as a wilderness area.