I'm a dog freak...I'm retired and do foster and am funding a small rescue in an area that has all kill shelters....this may be more than what you wanted but the first consideration to consider is is what part of town....
Second question is ON or OFF lease....if ON Google dog parks...there are some good ones including a couple of new ones...several of them were funded and or maintained by a corporate sponsor, Pet Safe...they have provided millions of dollars in support...their CEO Randy Boyd does great things for the community....
Before I relocated to Norris Lake I took my dogs to the Norris watershed and walked/hiked all over it....something else we would do is in the winter and spring before TVA would raise the water we'd go by boat to one of the many islands on Norris or Douglas and take a picnic and the dogs...they would have the run of the entire island........another great place OFF leash is beside the Clinch River coming out of the dam on the SOUTH undeveloped side....
ON leash just Google parks, walkways, etc...some really good places....I lived in Farragut for years and they have an abundance of places funded by the state, county and privately....Iam's Park is good...