Chris, I see you have some answers
on wpsmb, for Lone Pine Lake and the Meysan Lakes trail. Both are good. You can hike anywhere that is outside the Inyo National Forest's "Mt Whitney Zone" area. Here's
their map.And here's a map of the general Whitney Portal area:
Gmap4: Whitney PortalIf you are a little more adventurous, you can also leave the Main Mt Whitney Trail at the North Fork Lone Pine Creek crossing, and head up to Lower Boy Scout Lake. (Going beyond requires a day hike permit.) There is plenty of route information here:
Mountaineers Route infoOh, and there is always the fun little loop, hiking up the old trail to the North Fork crossing, where you could then descend the Main Trail for a one-hour or less loop. Here's the link:
Old Trail - Trailhead