Over the years, the Doctor has had some wonderful hats, each perfectly fitted to work not only with the rest of the Time Lord's outfit, but also with his personality.
As I write this on August 14th, I'm sure the Grand Moff and Peter Capaldi have already worked out what kind of costume will be worn by the Next Incarnation of the Doctor. But I still wanted to put in my two cents regarding his "Who-berdashery".
This is the look I would favor:
That 1950s vibe but especially that hat!
There are two actors I always think of when I see that hat. One is the French master comedian Jacques Tati. But as the Brits get touchy about any foreign taint to their beloved sci-fi hero (and I suppose quite rightly), I'll advocate for the other choice - Sir Alec Guinness.
Here are two pictures of him with the kind of hat I think would look perfect with the Doctor: