From your description, maybe figuring out how household objects work might be more interesting to him than typical toys. There's a great Usborne flap book for this age group, "See Inside How Things Work". For my DS, I accompanied the book with household objects that can be safely taken apart, explored and put back together (ex: ballpoint pens, flashlights). You can put together a box full of items to "fix" with tools you feel he can handle.
You mentioned chores...perhaps you can give him something around the house he can organize following some basic guidelines, and let him enjoy puzzling out the rest.
These type of activities allow him to work independently, but still require some preparation.
