>>2830677Turk Mountain is about an hour's drive from Charlottesville, Black Rock summit is maybe 30 minutes more away - downside being you have to pay 30 dollars to get on the road to access them.
The Rivanna River can be accessed in both C-ville itself and (more scenically) to the SE near Palmyra:
https://www.fluvannacounty.org/parksrec/page/trails-pleasant-grove
I've been in winter - quite nice - steeper than you might expect.
If you have a bike - the virginia blue ridge railway trail is maybe an hour's ssw of cville
And there's nice views off the appalachian trail if you ascend cole mountain (I recall the road as being quite rough - make sure you have an suv/truck for that one)
and yes, its an overnight, but you are right off 64 in cville and take it ~ 3 hours west and you get to new river gorge and there's obviously lots of stuff there if you haven't been - recommend beauty mountain - the parking is kinda confusing (part of a dirt road you can park off of - part of it there's signs saying not to) and the trail isn't marked or anything but the views are easily accessed
https://www.theoutbound.com/west-virginia/hiking/hike-beauty-mountain-trail
this has the best 180 view of the gorge ive seen