This post updated 3/14 with actual game times, more flight info, and removal of some unrealistic advice.
Should Stanford advance from the first two rounds, it will play in the Lexington regional. These games will be held in Rupp Arena on the grounds of the University of Kentucky in Lexington, Kentucky (map).
The games will be on Friday March 24th at 7pm and 9:30pm. Lexington's Blue Grass Airport (code LEX) is served by American and United. (Delta also flies there, but only from Atlanta, so any Delta flight originating in SFO has at least three legs and many hours.)
Alternatives are Louisville airport (code SDF) and Cincinnati (code CVG). Both these cities' airports are about an hour and a half drive from Lexington. Southwest airlines serves Louisville, so if you want to fly SWA, make that your destination. SWA has a 6:50am departure from SFO, arriving SDF at 3:50pm. There is theoretically time to drive from Louisville and make the 7pm game, but on the other hand, this would be a Friday evening.
There are American flights to LEX out of both SFO and SJC at 6:14am that arrive in comfortable time to make the 7pm game. No later departure would be assured of making the start of the first game. For a slightly more civilized departure time you could take an 8am flight from SFO on the Thursday.
Remember that the FBC Travel page has many useful links for scheduling flights.