The Louisville Loop Trail is not really a loop (yet). The most significant continuous portion runs from Caperton Swamp to Portland Wharf Park along the river. Current construction is causing a trail closure next to the Shawnee Golf Course, so Portland Wharf Park is a good starting/turn-around point right now.
The plan is to eventually have a 100-mile paved loop path around the entire city of Louisville. This is where the name "Louisville Loop Trail" comes from, but only about 25 miles of the trail are completed right now.