Everyone has there favorites and I'm a big fan of Horseshoe Meadows because you are at 10,000' and the hiking can be relatively easy or very hard. I love Trail Peak as a destination but I do it as a loop through Cottonwood Pass. I love the walk from Cottonwood Pass to Trail Peak.
One not mentioned above is the Meysan Lake Trail out of Whitney Portal. It is a gorgeous trail to many easy or difficult destinations, which is under utilized.
Your acclimatization is what you make it.
