Capitol View Park
13 miles of singletrack in Frankfort Kentucky
Capitol View park has 13 total miles of single track trail that follows the Kentucky River as well as several segments that follow along Glenn Creek Road and behind the Kentucky Library/Archives. It is maintained by https://kymbabluegrass.org/ and is a multi-use trail system. Be sure to look at the KYMBA website for trail information, maps, as well as closures and current trail conditions. They also have a Facebook page that you might want to follow so you're aware of any special events, such as bike or foot races as you'll generally need to avoid riding when major events are at the park.
The trails are well-designed, marked, and maintained. Consider them intermediate cross-country type of trails; there are roots, rocks, or ruts here or there, but very few difficult sections and offer a nice relaxing ride in the woods.
You will share the trails with runners, hikers, and deer, so always be on the lookout. Otherwise, there are few hazards, but always ride within your skill and fitness level. The trails that go behind the Kentucky Library are a fairly long climb up and have various steep sections of trail, so if you prefer a flatter ride, stick to the west side of the trail system.
I often say that I've never ridden the same trail twice at Capitol View because there are quite a few trails that branch off from each other or intersect, and it's quite easy to follow a different trail than you thought you were. While you might not know precisely which trail you're on at any given point, you also can not really get lost as you have the river to your west, the East-West connector (4 lane 55mph road) to your east that you can hear from most places on the trail, but you are also generally circling a large complex of softball and baseball fields and parking lots, so at any given time if you get lost, need to end a ride early, have a flat, etc, you're really never very far from where you parked. There are also many connectors between the softball/baseball field areas and the trails, so there are quite a few places as you ride that you could cut a ride short as needed.
This park does have quite a few Osage orange trees, so be aware of their fruit in the fall as it's softball sized and when it first drops it is hard as a rock and then later, it can turn into a squishy mess; neither are a lot of fun to run over if you're not expecting them. Thorns (and flats) used to be more common in the 90s, but I personally have not had a flat on this trail in many years.
I generally park near the entrance of the park itself, near a large Mountain Bike Trail sign, and I just do a loop around the west side of the park, which I would encourage for beginning to intermediate riders. Go clockwise around the park, and enjoy yourself!
Note that the trails HAVE changed this since video was taken, and the audio is terrible, but here is a video I personally took in August 2013 of Capitol View. https://www.youtube.com/watch?v=W6sZdXOPU9
And for the first time ever, I recently "rode the same trail" twice, in one day! A little exploring, but for the most part, did two identical loops of the west side of the park, including the top-right corner that I somehow always miss.

Please be respectful of our trails. Do not ride them when they are wet, check trail condition sites before going. Do not ride them on high-powered e-bikes, gasoline powered dirt bikes, horses, etc. Take in the scenery, and take out what you brought in.