It's been so long I decided to start all over and just play the love route.
(As an aside, the love route in Book 2 still is kind of sucky, because you have to do certain evil things you don't want to do to progress the plot).
Anyway, I just started Book 4. I go to train, and am told to come back tomorrow. I talk to Korra, I talk to Kya, I talk to Katara and the options end. I can't leave and I can't climb the tower and I can't figure out how to progress to the next day. I think I've checked every possibility.
Mind you, I played this previously so I obviously figured it out then, but I don't remember what I did to move this along. And the walkthrough doesn't cover Book 4.