I've sometimes done a Half Dome hike a week or so before heading to Whitney. Mt Dana at Tioga Pass is another one you could almost do in a loong day from the Bay Area.
Just remember, all the training you can do will not be enough if the altitude gets you. Acclimating for 24 to 48 hours before starting the hike will help a lot. Acclimating includes hiking above 10k and sleeping at least 8k, or better, 10k elevation.
