Our DD4 loves doing the Wilderness Explorers badges. Some do require parental help to write things down, but overall she hasn’t run into one that was too frustrating.
The Boneyard and the HISTK playground are wonderful places to burn off steam. I actually prefer the Boneyard because it is more open and easier to keep track of kids. There’s a lot of blind alleys on the HISTK playground where it is easy to lose a child temporarily. I just asked my daughter which she liked better, and she said that she liked the Boneyard because it has a sand pit. I don’t know if you’re staying on property, but the playgrounds at the resorts are also wonderful for kids. (And even if you’re not staying on property, if you happen to be at a resort for a meal, you can also take a bit of time to explore those playgrounds as well. They’re nothing more than just a normal playground, but my daughter loves them.)
We haven’t done Agent P yet (although my husband did it by himself while we were out of town), but if your child is a fan of Phineas and Ferb, I expect that it would be a hit. If your child doesn’t know who they are, it probably would be lost on them.
Going out to Rafiki’s Planet Watch is fun. A lot of the exhibits inside are very quick to skim by for that age group, but the petting zoo is fun, and if they have an animal encounter going on, that can be fun. (We got to see them feeding some of the lizards, for example.)
My daughter is the queen of impatience when it comes to stage shows. We were able to survive the Frozen sing-a-long because she knew the songs, but even then, it was pushing the limits of her desire to stay seated. As a result, neither Indy nor LMA are on our list (plus she doesn’t like loud noises).
For a longer trip, in Epcot, make sure you take some time at the jumping fountains in Imagination, near the exit for Captain EO (or whatever is there when you visit). When the movie is not letting out, you’ve got a huge area for a child to run around. My daughter prefers that to the Image Works area inside, and there are benches for parents. Also make sure that if you have the option to bring a change of clothes that you check out the splash pads in Epcot and the Casey Jr. water play area at the Magic Kingdom. Those are places where your DS could even enjoy getting wet. (Weather permitting, of course.)
The big hits for my daughter by park are:
Epcot: Living with the Land and the Gran Fiesta Tour (aka the Mexico boat ride)
Magic Kingdom: Philharmagic, It’s a Small World, Peoplemover, the Tiki Room
Animal Kingdom: Boneyard, Safari
Studios: Disney Jr. Live on Stage