Solder lake, just below The Major General, is a very nice place to hang out. You can climb class 3 up to the Major General and then on to Mt. Langley from there, although that is not the easiest. Most camp at one of the Cottonwood lakes and then hike to Langley from New Army or Army pass on the way to the other side..
Getting to Mt. Whitney from there is much more of a concern. It is estimated that a round trip from Sky Blue Lake to Mt. Whitney and back over Crabtree pass can take up to 12-14 hours. From Soldier lake it would not be practical to attempt Mt. Whitney in a one day hike. It is just too far away.
Go read Kashcrafts report of summiting Whitney from the Miter Basin. He has some pictures and links to discussion of the difficulty from Crabtree pass to Discovery Pinnacle up the dreaded sand hill.
http://www.mt-whitney.info/viewtopic.php?t=163