generalfrevious said:

I think it may be that no one ever heard Kane say rosebud.

We didn't see Kane's last conversations. He might have been mumbling Rosebud for days before he passed away.

As for Leia, I think we can assume the Alliance operated as a cell-structure. Leia was a key person in the Alderaanian cell, using her diplomatic cover to ferry communiques and materiel between "peaceful" Alderaan and its outposts on Yavin and Dantooine. After the destruction of Alderaan and the compromise of Dantooine, she may not have known any other safe place in the galaxy to hide from the Empire. Certainly she could not have directed the Falcon to any of the Core Worlds--the local Imperials would be waiting for them. That leaves the Outer Rim, where Imperial forces were scattered. I can't say flying to Yavin was the best possible decision, but given the finicky nature of FTL communications in Star Wars it may have been the only way to safely return to Alliance control.