I've got two of them - twins. Left to their own devices, they'll spend the entire day at w/es sitting at their PCs. Torn away from screens, they literally can't think of anything to do with their time. They'll tolerate half an hour playing Monopoly or cards with me but soon fight/get bored.
In warmer weather, I might be able to force them outdoors - though even this is debatable.
They browse (appropriate) internet sites, watch reruns of cartoons. One does at least do lots of writing his own stories and plays on computer. The other does a bit of programming and also some computer games.
Neither is sporty. They don't have wiis or DS or X-box but do spend most of their unstructured time at PCs. Neither does model making or lego or meccano. Neither does art/crafts for fun.
What else do 11 yr old boys do? We don't live in an area where they can safely go out alone. Their friends are driving distance away and there's also an issue with friendships anyway right now, as these are breaking up/ reforming etc as they're all in senior school and more dispersed.
When they recently had 2 friends round, it was clear that all 4 had trouble knowing what to do with their time. A bit of screens, a half-hearted game in the garden but clearly even the friends were bored.
In the 21st century, if you're NOT sitting at a screen, what do you do indoors, as an 11 yr old boy - especially, what do you do if your parent/s don't have time to 'entertain' you?