This is mostly stuff that all ages can do that children aren't kept out of.
With GT they can play foosball, darts, cards and don't wake the llama. They can have clubs based around playground, swimming, homework, games, voidcritters (kids room stuff pack). Oh, and also the arcade game.
With OR they can roast marshmallows and other things if an older sim starts a fire. They can play in the tent. They can collect bugs in addition to frogs. I think they can hike. They can play horseshoes.
Base game activities that they can do besides playground equipment includes swimming, chess, fishing, collecting.
Did the consoles come base game or in a pack? Multi player video games are a fun group activity with kids. Also watching movies if you have movie stuff.
Seasons has so much, egg hunts, presents, holidays, skating, snowpals (With which they have extra interactions older Sims don't), snowball and mud fights.
Which stuff pack came with the water slides, was that called backyard stuff? Anyway they're fun. And kids can play in the toddler pools that either came with that or seasons.
In city living, you can get the spice hound or chopstick traits while in the child stage. Children can use the singing skill also, though I haven't ever tested whether they can use the karaoke machine.
I may think of more later. I play with a lot of children.