Where did Bran go during the Battle of Winterfell?

Bran guided a dragon

Well, maybe he's tried? But if that's the case, he does not seem to have succeeded. We did not see him establishing a direct link with any of the living or dead dragons, or whether he was able to alter their flight plans. Nor is it clear that he helped in any way when they were fighting low visibility. So … probably not.

Bran used the Weirwood network to search for objects

Possible. Usually, Bran needs to touch the shrub to do this, but he may not need to touch it as long as he has proximity. He could have paraded past, present, or future visions. Or perhaps he was following the battle from several points of view, as a form of omni-recognition. (Although if so, who did he report it to?) Perhaps he was recording it for posterity. Or maybe it was fully verified and was considering the escape of a trailer for episode 4.

Bran used the Weirwood net to change the past

Theoretically possible, but unlikely. Bran learned his lesson with Hodor and he was heartbroken. Admittedly, he does not express so many human emotions now, but he does not seem to be interested in getting involved in the matter. He does not often give out spontaneous information and treats most people – Jaime, Theon – as if he's so far beyond what they've done to hurt him that he's not even recording anymore. What past does he care about changing if he does not care about his?

Bran plugged in to help attract the king of the night

Ah … probable! Time and time again, in these last seasons of "Game of Thrones", Occam's old razor proposal comes into play: the simplest explanation is the one that is most likely to be correct. All conspiracy theories so loved by fans usually turn out irrelevant. Remember the theory that Arya was really Waif? Or that Littlefinger was not really dead? Or that Bran, himself, was the king of the night?

The books encouraged fans to play detective and to deduce clues that, after all, could support many readings. But the spectators of the series have not shown much interest in playing this game. The simplest and most likely explanation is that Bran is easier to locate when he is in his psychic space and that he was trying to serve as a bait; he stopped when the king of the night was rolled up. This would not be an explanation that would satisfy the most conspiratorial fans, but they probably should not expect the show to widen its mysteries when it tries to close shop.