Horseshoe Meadow and Onion Valley are the two main places for acclimatization. I like the former because it non-taxing and the latter because its magnificent views from the pass.
My guess is you haven't taken seen all there is in these areas.
Horseshoe Meadows...Go to Trail Peak, I was blown away by the views from this peak earlier this year.
Onion Valley...Robinson Lake is an ok hike.
Why leave Whitney Portal...
Hike the Meysan Lakes Trail...the upper part of this is extremely pretty and as challenging as you want it to be.
