I'm starting to lean towards an adventure I create -- although after 20 years away from D&D, I think a premade adventure module might be a helpful crutch. I'm very open to suggestions, please.
As background, I shy away from undead and particularly foul aberrations, and situations where slaughtering humanoids is the expected way to deal with a situation (although you might find some contradictions to that below). I also avoid thorny moral dilemmas (i.e. choices between two possibly evil actions), but seek out ethical and other dilemmas to present (diplomacy vs. violence, trust vs. distrust, money vs. law, etc.). My favorite opponents (using some 3e terminology) tend to be constructs, vermin, plant creatures, oozes, and elementals, and really "monstery" things like cloakers and ropers, because they're relatively guilt-free.
One of my favorite 4e rules for playing with kids is that you never have to kill anything; you can always choose to knock opponents unconscious. You can, of course, house-rule 3e the same way.
OK, 4e adventures that might be suitable for children with little to no modification:
1st level
Kobold Hall (DMG)
Stick in the Mud (Dungeon #171)
Death in the Pincers (Dungeon #172)
Into the Shadowhaunt
The Scorpion Queen (In Search of Adventure)
Legacy of the Labyrinth (In Search of Adventure)
2nd-4th level
Treasure of Talon Pass
Menace of the Icy Spire (Dungeon #159)
Fool’s Grove (2-1/2) -- great for kids!
Remains of the Empire (Dungeon #165)
Stormcrow Tor (Dungeon #169)
7th level (there are some gaps in level coverage)
Treed (Dungeon #171)
Danger at the White Lotus Academy (Dungeon #165) -- great for kids!
Rift of the Hill Giant Thane (Level Up #1)
Heart of the Forbidden Forge (Dungeon #167)
10th-12th level
Hall of the Snake God (Dungeon #169)
The Longest Night (Dragon #370)
The Haunting of Kincep Mansion (Dungeon #156)
Dark Heart of Mithrendain (Dungeon #157)
14th-15th level
Alliance at Nefelus (Dungeon #165)
Sea Reavers of the Shrouded Crags (Dungeon #158)
Throne of the Stone-Skinned King (Dungeon #166)
18th-25th level
Summer's End (Dungeon #160)
Winter of the Witch (Dungeon #162)
Tomb of the Sand King's Daughter (Dungeon #160)
Most of these assume you have a DDI subscription, but others are free on the WotC Website or come from Goodman Games products.