At Oxford, a couple of months ago, he gave his first public talk since retiring as CEO. There he mentioned he's currently not doing much, but he's researching a few problems to do with governance, healthcare and the environment. He said he doesn't want to try to do anything like Microsoft again, because anything like that would inevitably pale in comparison. He seemed more interested in charity/politics/similar.
For years he's been trying desperately to buy an NBA team and bring it back to Seattle to revive the stolen Sonics. So far each time he has tried, (the Sacremento Kings, Minnesota T-wolves, among others) a local billionaire or the hometown has stepped in to deflect his offers.