I am so spoiled... took my children there so many times it is imbedded in their psyche! The greatest kids museum - handson, kid friendly & a re-creation of the original Piggly Wiggly. I have yet to find a comparable experience - and I've tried!
I believe the Pink has also expanded - but the original is an actual mansion donated to the city - and they have done the legacy proud! It is a must see!
Believe it or not - on a good Sunday after church - you can take your children to Beale Street. It's minus the evening party crowd - with great food and sightseeing. I took my kids to the Hard Rock and we listened to good live gospel music. They were thoroughly entertained!
There is plenty for your family to do. You can visit Liberty Land Amusement Park, Graceland, home of Elvis Presley,there are botanical gardens tons of museums including Mud Island, you can visit Sun Studio and take a tour of it, there is an IMAX, you can tour Cordova winery and much much more. There is also "Memphis in May" only the biggest BBQ event ever! All of this and I haven't left Memphis yet! Your family will find plenty of art museums etc. I know you will find plenty to do with your family!
1) riding the trolley
2) watching the entrance/parade of the ducks at the Peabody (I think it's at 10 am each day). You will ask yourself, is that it? But kids love it.
3) cosmic golf in the little mall area - Peabody Place
4) Redbirds games
5) Grizzlies games
6) Gibson Guitar Factory Tour (see how guitars are made)
7) Jillians is a huge arcade in the Peabody Place (make sure to take children during daytime it is more of a barcade at night)
If you are looking for water parks or sports, I guess the best bet is to make friends with boat owners. Many people go to the lake in the summer (Pickwick in MS/TN is one of the closest).