Take it from someone who spent 5 1/2 years there, Clarksville is a crappy town. Make the drive to Nashville, you will enjoy yourself much more.
If you do insist on staying in the Clarksville area, there are a few things to do.
As far as gunshops go, the best in the immediate area is The Shell Shop in Hopkinsville. They have an indoor range that is very inexpensive, albeit small (two lanes). They also have a modest selection on hand, but their prices are reasonable. The are located across from a bike shop behind Applebee's on Hwy 41A, just as you come into town from the south. The Applebee's is dircetly across from Wal-Mart.
There aren't too many gunshops in Clarksville / Oak Grove. There is Grandpa's on Hwy 41A, but they don't stock too much. Lightfighter Tactical in Oak Grove is a must-see. Other than that, there are mostly pawn-shops, which are scattered around town. The pawn shop with the best selection will most likely be Eagle Pawn on 41A. Be forewarned, looking at their price tags can feel like you're being raped.
For food in Clarksville, there are a lot of chain selections, but not much in quality, free-standing, independant restaurants. If you like Mexican, Pancho Villas is the place to go. It is located directly across from Ft. Campbell's Gate 4, between U.S. Cavalry and Lightfighter. If you go for lunch during the week, be prepared to wait a short while, due to the large number of soldiers who eat there. Their salsa is worth it though.
For entertainment, don't bother, drive to Nashville. There is nothing in Clarksville besides the mall, the movie theater and a couple strip-joints (and neither of those is populated by overly attractive women).
If you do drive to Nashville to check out guns, you'll have a much better selection. Here's a short list of what's available, and where they are located.
Academy of Self-Protection - Joelton, exit 35, I-24
Gun Mart - Charlotte Pike
Sporting Arms - Charlotte Pike
Gun City - Murfreesboro Road
Goodlettsville Gun Shop - exit 96, I-65
Guns and Leather - Greenbriar, exit 98, I65, then north a few miles
The Reloader's Bench - Mt. Juliet Rd., I-40 east to Mt. Juliet exit
On Target - Thompson Lane, Murfreesboro, I-24
Franklin Gun Shop - Franklin, I65S to exit 65
Steve's Gun and Archery -Columbia, I65 to exit 46
Specialty Arms II - Lavernge, I24 to exit 66?
Hope that helps.
Frank