He certainly didn't need a lot of sleep - not by human standards, anyway - but he couldn't go forever without, either. Eventually, he got tired. Eventually, he needed to go the hell to bed.
When eventually rolled around, he was left with a choice. He could go back to the TARDIS, which had infinite space, and damn near as much possibility for people who could have a key and come waltzing in, or he could have a hotel room with less physical space and chance of having unexpected (and possibly unhappy) company.
He was worn the hell out, from talking to past and future and alternatives to the people he'd loved and lost and killed and hated and fought with and, apparently, fucked or been fucked by and oh, what did it matter? He just wanted somewhere to curl up, go to sleep, and be left in peace.
Which did not explain how he ended up passing by a lot of completely empty rooms to go to Professor Yana's.
Maybe he was more self-destructive than he thought, but he didn't really want to be alone and of all the people here, Professor Yana was who he felt
safest with. So, he let himself into his room. He crawled into his bed and curled up facing the door. He fell asleep waiting for the old man to get back.