Hi 63,
I cannot help much with the camping issues. I "camp" at the Quality Inn in Mammoth, and the Comfort Inn in Lone Pine.
For your family, Mammoth Lakes will be far better than Lone Pine or Bishop. Mammoth Lakes has many options for restaurants, shopping, etc...
Also, many "easy" day hikes for them to enjoy (if they are of a mind). Crystal Lake is an easy 1/1.5 hour hike from the parking lot above at Lake George (30 minute drive from Mammoth Lakes). Not too much elevation gain, and easy trail to follow. Also gives access to Mammoth Crest if they are more adventuresome. See:
http://www.yelp.com/biz/crystal-lake-mammoth-lakes for more details. Both of these hike would be good choices for acclimatization/warm up. A more aggressive warm up hike would be from the lodge to the top of Mammoth Mountain. There is a trail, or if more adventuresome you can simply hike up the ski runs (assumes no one is skiing down the runs).
The Devil's Postpile is OK, but you are in a valley, and while the geology is interesting not nearly as inspirational as the views from other hikes.
Another option in the Mammoth Lake/Mt. Dana area is Saddlebag Lake. See:
http://www.summitpost.org/saddlebag-lake-loop-trail/645638 for more details. 6 miles, nearly flat hike. Might be good for the family? You could drop them, and head for Mt. Dana. Saddlebag Lake is ~ 30 minute drive from Hwy 120, so allow an extra hour for your drive to Parking for Mt. Dana. Saddlebag Lake also offers other more aggressive options. North Peak for instance. Bit of a scree slog, but good adventure. Trail is not well marked, so be prepared to find your way. Family does the loop, the guys go for North Peak. There is a store/restaurant on the Lake, and you and your family can save the 1.5 mile hike around the lake, and enjoy a boat ride across the lake for $7.00 each way, or $12.00 round trip. WARNING - Bring mosquito repellant.
If you do Mt. Dana, you should drive the 20 minutes to Lembert Dome, and climb to the top. See:
http://www.summitpost.org/lembert-dome-s-south-slope/22416/c-158258 for more information. This link shows the route up the class 3 south face.
If you family has the car when/if you do Whitney or Langley they might like to drive to Death Valley. You can only look at "Nick-Nacks" for so long in Lone Pine. Not sure how far that would be, but might be interesting. Others can give more information on this option.
Enjoy!
John
Edit: I should have added that there is still lots of snow at Mammoth. See
http://www.mammothmountain.com/MyMammoth/WebCams/ for web cam views. My guess is that Saddlebag Lake area also has lots of snow. Of course, you do still have 10 days, but unlikely that snow will be gone.
