Mammoth is home to some incredible, minimal effort hikes at moderate altitude. GREAT choice!!
San Joaquin Ridge from Minaret Vista*****
Duck Pass from Lake Mary*****
Mammoth Crest from behind Lake Mary****
Shadow Lake from Agnew Meadow****
Rainbow Falls and Devils Postpile***
Convict Lake up to the creek crossing****
(Ratings are my own)
Good choice on moderate elevation for the first night, at least, as well. While sleeping high (Barcroft or Mosquito Flat) can help, if you shock your bod right off the bat you're going to be miserable for your Whitney day. Primarily, you probably won't be able to actually, well, SLEEP.
Plenty of fun to be had around here, as well, in terms of lower-energy, ease-into-it sort of hikes:
Piute Pass from North Lake
Lamarck Lakes from North Lake
Blue Lake from Sabrina
Treasure Lakes from South Lake
Bishop Lakes/Pass from South Lake
Green/Brown Lakes from South Lake
Kearsarge is also one of my, and a LOT of other people's, fave areas. Lots of company up there, and good fishing! Robinson Lake from Onion Valley will take you away from the crowds.
If you'd like pics to give you ideas, let me know.
Best of luck on your adventure!
-Laura
PS: Just thought of another area of "something different" in the "northern" reaches (since you're going to be in Mammoth, it isn't that much further). The Bodie Hills are an incredibly diverse, open, and lonely place, all around 9K+.
Pics here. 
