If I were going to stay just at the resort... and had the money for a deluxe... I'd stay at Animal Kingdom Lodge in a savannah view room.
Now, we always rent a car for our Disney trips, so if you're going to be depending entirely on bus transportation, that may not work out so well for you.
But for us, the ability to sit out on the small balcony with a bit of breakfast and watch the animals strolling by? It's priceless.
My little guy is 4, and he's animal-obsessed. He loves water, but isn't really a "swimmer" on his own yet. I'd love to take him to Beach Club or Yacht Club to enjoy Stormalong Bay, but... not yet. When he's bigger and can truly swim, that's on our to-do list. For now, we love the pool at Animal Kingdom Lodge. It's more manageable for keeping an eye (or a hand) on my little guy while he's still learning...
As for what to do, there's a lot of stuff to do at any of the deluxe resorts. There are activities of all sorts going on all day. At AKL, they do everything from arts and crafts activities to storytelling to animal feeding time to an end-of-day parade for the kids. Near the pool, there's a small playground that my son really enjoyed at 3 1/2. If you don't have a savannah-view room, there are viewing platforms (some with rocking chairs to sit in) for looking at the animals scattered through the resort. In the evenings, there are night-vision goggles available for watching the animals settle down for the night. And more...
From there, I'd resort-hop around to other resorts for some meals and a change of scenery. I'd probably hit Downtown Disney as well, let my son play a bit at the
Lego store, grab a bite there, etc. You could also do a day (as others have suggested) at one of the water parks. Either way, to me, Animal Kingdom Lodge makes the vacation feel more unique - thanks to the theming and the presence of the animals, it's more than just a hotel room and a pool, if that makes sense. (Because you can stay off Disney property for far less, if all you want is a room and a pool!)