I can't talk to him. There's no icon over his head, and the "Talk To" menu doesn't come up when I approach him. Am I doing something wrong, or is this a known bug?
Have you talked to Admiral Quinn first? Talk to Quinn first and he will allow you to talk with Sulu. Also, try you "contact Starfleet" (looks like a communicator badge) on your map, in the upper right. If Sulu has a mission available to you, then you'll see his name available.
Also, ensure that the NPC has a "Q" above their head. A "Q" means they have a mission for you, iirc.
Look at your mission objectives on the right of the screen. is there a blue objective?
This happened to me recently, you just need to make sure you talk to the Admiral and go through all his choises, there is a mission you need to complete by talking to him that doesn't let you talk to sulu until you finish it.