My family spent a week in Jackson, TN in spring of 2010. I loved the southern charm that this city offers. There is plenty of small town feel and friendly people. It's proximity to the large city of Memphis puts nightlife about an hour away.
Don't worry too much about Memphis. There is so much to do in Jackson, TN that families won't get bored. Local celebrities include the railroad engineer named Casey Jones. An entire museum is dedicated to his honor. It's a 'must see' stop. My kids really liked seeing all the train items that are on exhibit there.
There are historic locations throughout the city that are perfect for families to enjoy. One that my family particularly liked is the Cypress Grove Nature Park. It has a lake, pond and 7,000 ft boardwalk. The Raptor Center there is home to birds that have been injured and can't be returned to the wild. The kids had a great time and admission is free.
Family centered restaurants are plentiful in Jackson, TN. These range from brand names to fast food and mom and pop types of places. As you can tell, we can't wait to go back again.