I just finished reading AFFC Brienne VII again. In that chapter, she's at the Crossroads Inn, and also as a crossroads in her path. She puts her things in her room, and plans to leave early the next morning, taking Pod with her, but ditching Hyle and Meribald.

"Where will we go, ser? I mean, my lady?" asks Pod while they are in their room.

Brienne can think of four options, all in different directions:

Brienne had no ready answer for him. They had come to the crossroads, quite literally; the place where the kingsroad, the river road, and the high road all came together. The high road would take them east through the mountains to the Vale of Arryn, where Lady Sansa's aunt had ruled until her death. West ran the river road, which followed the course of the Red Fork to Riverrun and Sansa's great-uncle, who was besieged but still alive. Or they could ride the kingsroad north, past the Twins and through the Neck with its bogs and marshes. If she could find a way past Moat Cailin and whoever held it now, the kingsroad would bring them all the way to Winterfell.

Or I could take the kingsroad south, Brienne thought. I could slink back to King's Landing, confess my failure to Ser Jaime, give him back his sword, and find a ship to carry me home to Tarth, as the Elder Brother urged. The thought was a bitter one, yet there was part of her that yearned for Evenfall and her father, and another part that wondered if Jaime would comfort her should she weep upon his shoulder. That was what men wanted, wasn't it? Soft helpless women that they needed to protect?

What way would she have gone had the Bloody Mummers not intervened?

Of course, we know, no matter how tempting, she wouldn't take South Road, no matter how tempting. We also know it wouldn't achieve what she wants anyway, because Jaime is actually, around that time in the Riverlands, likely heading to Riverrun, and hence at the end of the second, the western choice, not the southern one.

What could have happened if Brienne arrived at Riverrun for the siege? That's an option that was kind of explored in the show, albeit in a completely different context.

Perhaps she would have gone east would she have arrived at the Vale. She may have arrived in time for the tourney, but would she have had the information necessary to work out what Baelish was up to? She knows Sansa as a highborn girl with auburn hair, and would have no reason to know he didn't have a natural daughter, but she still could have uncovered the conspiracy around Tourney very much in the style of Dunk and Egg in the Mystery Knight.

Or perhaps she would go North, which could possibly end badly, particularly if she heard word of Stannis, and decided to take the revenge path instead, or met any of the Ramsay men or other ruffians up there. Or maybe she would have found herself embroiled in whatever eventually happens up there.

It's food for thought.

Also, one other thought that occurs to me from this chapter (and the next, but I haven't got to that yet): The BWB capture Brienne, but they let Meribald go to continue on his journey. Perhaps it is he who gets help from the Quiet Isle, or somewhere else.