In the HBO TV series Game of Thrones episode Blackwater, the Hound offered to take Sansa to Winterfell. The ending of the scene was ambiguous and I thought she left King's Landing with the Hound. However, in the next episode she's still in King's Landing. Perhaps in the books there is a better description of events, but I do not think they explained Sansa's thought process very well in the TV series.
In the episode Sansa is under the impression that the city had fallen to Stannis Baratheon's forces. King Joffrey made her suffer in previous episodes, and during the Battle of Blackwater, no one was watching Sansa and she had an opportunity to escape. Why did Sansa stay in King's Landing after all she endured?