Don't overlook the Vivian Creek Trail on San Gorgonio. Very steep (the first section of the trail) and a butt-kicker for a day hike. I actually hiked this trail about a month after I went up Whitney for the first time (first week in June - just like you!) and was impressed with the difficulty.
One important tip: reduce your training down to almost nothing for a few days before your hike to let your body recover from the intense training.
