Animal Crossing looks like a good possibility.

The Harvest Moon games are delightful. They are cutesy farming sims that encourage planning ahead and reward experimentation with the game mechanics. They're less about exploration than about resource management, though.

Viva Pinata is a weird life-simulation/resource-management game that flopped on the 360 because it is too kiddy for teens and too deep for kiddies -- breeding some of the larger pinata species requires satisfying a head-spinning number of preconditions...but it's really cute.

Again, not really exploration. Hmmm.

If you mean "sandbox" in the sense of "walking around whacking stuff to see what happens" then Oblivion might qualify. It's a truly enormous fantasy RPG in an immersive and interactive world. But it may be too complicated for the wee ones. I think you can actually toggle the gore, though. But don't quote me on that -- that might have been another game. The game does use words you might hear in prime time like "damn" and "hell" and it does have booze and wenches, as befits any fantasy title.

Seems like there'd be a big ol' Pokemon-type MMO for youngsters. There may be, but I don't know about it.

*on preview*

You're right -- Animal Crossing would be perfect.

I've heard good things about Animal Crossing.
I also really like Oblivion, but I'm not sure how Sandbox that is for you.

These are some great suggestions, thank you. I neglected to mention that we have a PC too.

I'll third Oblivion. It's big, open ended and there are a lot of mods for it that increase the dungeons and towns and improve the landscape. The add ons, "Knights of the Nine" and "Shivering Isles" are good too. "Isles" adds basically a new, small island to wander around on and a really annoying god, but aren't they all?

The suggestions on GameSpot say Stalker. I say no to that. It's story-driven and not a sandbox. At one point when you enter the city, you can't go back. I actually haven't finished the game as it pissed me off so badly. Also, to get to the very end scene you have to apparently go through 15 separate firefights for no real reason other to drag out the end of the game.

Oblivion is pretty wow, though. If you get the PC game, make sure you've got a good video card. The minimum specs that they recommend won't run the game, and if it does you'll have to turn off so many features (shadows, grass, water, high and medium textures etc etc) that it becomes pointless to run it. I've got a GeForce 7600 512meg card and a gig of RAM and it does the job nicely, though I can't have everything maxed unless I want the frame rates to drop.

Also, how about Neverwinter Nights 2? D&D with not so much violence, as it were. In Oblivion you can, if you wanted, kill almost every living NPC in the game and if not that, there's still bandits to kill, so can get a little iffy. With NWN, you're mostly fighting orcs or spiders or the like, and the bodies fade out after death.

Spore will probably be really good for what you're looking for, but we still have to wait (impatiently) for that.

Check out Banja. I had a look at it a few years ago, and it looks like it's still going strong. Puzzles, exploration and no killing. Bright colours and a really neat environment. And it's free and online. Click on the "Guide" button for an overview of the story and the characters that inhabit the island of 'Itland'. To quote the site, There is no conquering here, but the discovery of mysteries of an enchanting world. The unifying thread of Banja’s whole story is the harmonious life of the isle’s citizens that one must try to preserve in spite of the arrival of troublemaking elements…

Dofus is an MMORPG that is pretty nice. There's fighting, but it's not violent (no guns, blood, nasty death scenes). The artwork that you see on the site is the exact artwork used in the game - stylized and bright. It's not free though.. $6.90USD/month.

Burnout Paradise for the 11-year-old, one of the Harvest Moon games for the ten-year-old, Animal Crossing for the seven-year-old.