Headed there next week for a business trip and will have some time to kill.  TIA.

I hear Liberty University has a cool shooting range.

Not yet on the range... probably will be a while longer on that one.

I live in Lynchburg.... having a hard time thinking of much to do right now.  There are a bunch of trails around for walking/hiking, if you like that kind of thing.  Snowflex on the mountain across from Liberty, is a small ski/snowboard slope made out of something that's supposed to replicate snow.  There's an indoor shooting range at Lynchburg Arms, it's only 25 yards but you can shoot just about any handgun or rifle in there.  The D-Day Memorial in Bedford is supposed to be pretty good.  There are some pretty good restaurants around.

Right now is kind of a bad time of year, as a bunch of stuff to do here is out of season.  If I think of anything else, I'll add it.

Any decent gun shops in the area?

Black Dog Sporting Goods
Lynchburg Arms

Lynchburg downtown has been revitalized and is nice place for a stroll to visit the unique shops and restaurants along the James.  As mentioned there are a lot of trails within the city and then all over the nearby national forest.  The Blue Ridge Parkway is scenic and easy too.  Jefferson's Poplar Forest is interesting look into colonial living in the area. Good brew exists, but you have go to the breweries which none are located in the city.

You might like hiking to the WWII B-25 Crash Site

There's some good festivals, but I'm not aware of anything this early.  Also some decent concerts venues, Phase II, Ellington Blues House, Sedelia, but someone more local would have to tell you the latest and greatest music offerings.

As far as gun shops, it's an area where a lot of guns are still sold FTF.  The only FFL that I've used in the area is Amherst Arms(Madison Heights), which had good prices and ok inventory, but keep in mind nearly all LGS there cater to the hunter and archery is a big deal.