I have spent some time recently exploring the North Bank and Buttermilk trails again. These are a pair of well maintained trails owned by the James River Park System. Though the trails do not technically make a loop, you can connect from one to another to make a loop.
On my most recent hike, I started at the pipeline trail and then went to the North Bank section. Once I finished the North Bank, I took the Boulevard Bridge (aka Nickel Bridge) to the start of the Buttermilk Trail. From here, I followed the trail to Belle Isle and crossed the suspension bridge to get back to the pipeline. The pipeline is not a necessary part of the loop, but I find that it is an easy add on.
If you want to try this loop, please be advised that mountain bikers also use this path. Be aware of your surroundings and do not crowd other people while on trail. Also, clean up after any furry friends on trail!