Tonks is probably agonizing over her relationship with Lupin likely looking for any news on Lupin and his dangerous mission (that Dumbledore assigned to Lupin).
Half-Blood Prince chapter A Very Frosty Christmas
“Tonks’s Patronus has changed its form,” he told him. “Snape said so anyway. I didn’t know that could happen. Why would your Patronus change?”
Lupin took his time chewing his turkey and swallowing before saying slowly, “Sometimes . . . a great shock . . . an emotional upheaval . . .”
“It looked big, and it had four legs,” said Harry, struck by a sud- den thought and lowering his voice. “Hey . . . it couldn’t be — ?”
Half-Blood Prince chapter A Very Frosty Christmas
“I’ve been living among my fellows, my equals,” said Lupin. “Werewolves,” he added, at Harry’s look of incomprehension. “Nearly all of them are on Voldemort’s side. Dumbledore wanted a spy and here I was . . . ready-made.”
Half-Blood Prince chapter A sluggish Memory
“Not great,” said Harry, and he told her all about Lupin’s mission among the werewolves and the difficulties he was facing. “Have you heard of this Fenrir Greyback?”
Half-blood Prince ch. The Unknowable room
“The Prophet’s often behind the times,” said Tonks, who didn’t seem to be listening to him. “You haven’t had any letters from anyone in the Order recently?recently?”
“No one from the Order writes to me anymore,” said Harry, “not since Sirius —”
He saw that her eyes had filled with tears.
Half-Blood Prince chapter The Phoenix Lament
And the meaning of Tonks’s Patronus and her mouse-colored hair, and the reason she had come running to find Dumbledore when she had heard a rumor someone had been attacked by Greyback, all suddenly became clear to Harry; it had not been Sirius that Tonks had fallen in love with after all.
Looking at the map of the 7th Floor there are plenty of corridors. If she came from Dumbledore's office and heading in the direction of Gryffindor then she would be heading down the corridor to the Gryffyndors.
http://thehogwartians.tumblr.com/HogwartsMap
She might be going to the Gryffindor common room in the hopes of looking for anyone of the Weasley's with letters from the Order and hopefully a bit of additional news about Lupin.