Ditto Duck Pass, and you can cut it short if you're not feeling strong the first day or two, just go to Arrowhead, or Skelton, or Barney and turn around if you're not up for the pass. This will still get you a lot of time above 9,000 ft range. Or you can just do one short lake hike after another like McCleod or Heart or TJ, so many options there in Mammoth. That's usually enough for me the first day coming from sea level after a long drive and all the stress of getting way.
Duck Pass is a steep climb at the end with great views. You can go on to the Mammoth Crest, even make a loop back to Horseshoe Lake if you're up for a longer hike. I also like Shadow Lake and a little beyond, but you have the hassle of the shuttle bus to get to Agnew Meadows and back.
Personally, coming from sea level, I like to spend the first day doing 2 or 3 short lake hikes in the 9,000-9500 ft range described above, and spend the second day at Little Lakes Valley up Rock Creek Rd at 10,000+ ft - not too much climbing. Easy to spend a whole day there at lake after lake, maybe catch some trout. If you want to go higher quickly, head up Mono Pass and hit Ruby Lake along the way.
Another great option is to spend time in the Cottonwood Pass area, hanging out at the day use/camp area ~10,000ft and climbing trails to the pass or beyond. This is a great last day before getting some rest at the Portal before Whitney. As the old saying goes - climb high, sleep low.
This regiment might seem slow to the typical young weekend warrior coming from sea level to claim that Whitney trophy, but it makes sense. As I get older and smarter, I'm allowing more and more time to acclimate, it makes everything more enjoyable.
Have a great trip.
