Warrior's Path State Park, located just outside of Kingsport, TN, has just about everything you can imagine in a park: golfing, swimming, fishing, boating, camping, hiking, horseback riding, mountain biking, picnicking, as well as playgrounds, tennis and soccer facilities. For years I would go to Warrior's Path for cookouts and a stroll around Duck Island, never realizing the extent of all the other opportunities that existed. The website above contains directions to the park along with a park map. Here is a link to the old hiking trail map, which has more detail than the current map on the website.
Warrior's Path has the very best playgrounds in the Tri-Cities. It's called "Darrell’s Dream Boundless Playground" - it is "a place where children of all abilities can learn and play together."
In terms of hiking, there are many opportunities. 1) The Holston Bluffs Trail is a unique 1/2 mile loop that takes you down to a secluded beach on the river. The trail head is located within the Overflow Campground which is to the left before you enter the park itself. 2) The Overlook Trail, takes you 1/2 mile through the forest to a nice view of the lake (and I-81) below. To reach this trail drive through the park, past the marina, immediately before the final boat launch turn right and go up the hill. Park at the soccer field and you will then see a trail head to the left (you could also walk up the old farm road). Here's a view from the overlook. 3) The Fall Creek Loop Trail can be accessed from the back of the park. The road to this back parking lot is rough (high clearance vehicle strongly recommended) and spaces are limited. It's located off of Childress Ferry Road (map here). You can also get to this area of the park by hiking in on the Devil's Backbone Trail. 4) There are numerous other trails to explore too many to list!