There is so much to do at Shelby Farms park, and it is so much bigger than people seem to realize when they visit it.
It has the largest off-leash dog park in the city, with acres upon acres of open area which includes 4 lakes. The hiking trails at the dog park come out to about 3.5 miles total. There aren't many benches on the western park of the Outback (which is what the off-leash area is called) but those lakes are usually the least crowded. The eastern lake has several benches around it but is often becomes very crowded on that side, so if you have a dog that tends to get over excited with lots of dogs around I suggest staying on the western side.
The park itself has lots and lots of hiking and running trails. The Chickasaw trail is still open, even with all the construction, and is a nice walk/jog at about 2.85 miles. There is also the Tour de Wolf bike trail that many people hike/run and that comes out to about 6 miles.
There is a 6.5 mile Greenline that runs from the edge of Shelby Farms all the way to down town that is awesome for running, especially if you are looking for something extremely flat. It patrolled daily by 2 officers on bikes, and is generally safe.
Outside of the park itself you have the Agricenter which hosts the camp ground, farmers market and a decent nursery.
Over all the park is amazing and totally worth visiting, especially if you are traveling with dogs and they need some leg stretching.
One note, be sure to check the Shelby Farms website to be sure there aren't any events that might close off areas of the park. For example, some road races are held there as Shelby Farms hosts several USTAF certified courses that many area business and running clubs utilize on a regular basis.