August Edinburgh is a different city. The Old Town is impenetrable, every pub has a queue, and the locals have mostly fled. It's spectacular but it isn't really Edinburgh.
November is when you see what's actually here.
The Light
Edinburgh in November has a low, golden, almost horizontal light that arrives in the late morning and is gone by half three. For those few hours it does something extraordinary to the castle, the closes, the Firth of Forth on a clear day.
Bring a camera. Set an alarm.
The Pubs
Without the August crowds, the old pubs on the Royal Mile are actually usable. The Jolly Judge, tucked down James Court, feels like it hasn't changed in decades in the best possible way. The Bow Bar on Victoria Street is smaller than you think it will be and better than you expect.
A good Edinburgh pub on a grey November afternoon is one of the finer things in life.
Arthur's Seat
The hill in the middle of the city. In summer it's full of tourists in entirely wrong footwear. In November you'll share it with locals walking dogs and the occasional runner. The climb takes 45 minutes and the view from the top on a clear day is implausible — the whole city, the Forth, Fife in the distance.
Wear shoes with grip. The basalt gets slippery.
The Cold Isn't As Bad As People Say
You'll need a proper coat and layers. But November in Edinburgh is often crisp and dry rather than the relentless grey wet that February brings. Come prepared and you'll find it bracing rather than miserable.
The city suits the cold. It was built for it.