In the Lone Pine area I suggust Boulder Creek RV park just south of town on 395. The best RV place in the Eastern Sierra. Many pull through sites with sit down views of Mt. Whitney and the Sierra Nevada and to the east the Inyo Mtn. You will see F18's from China Lake buzz the valley floor on a daily basis doing their training runs. Some sites have concrete pads to step out on, nice clubhouse, pool, showers and store. My favorite site is #74 (end spot, pull through, concrete pads and views of Whitney. Take in the Lone Pine Film Musuem while there and it's a great place to stay if you want to do a day trip into Death Valley.
In Bishop I really like Brown's Town. It's just south of downtown next to the golf course. Try and get a site towards the back on the golf course side. It is a bit noisey due to being just off 395 in town but you can walk to everything. Jack's Waffle Shop is the best for breakfast, Schat's world famous bakery and Whisky Creek for lunch and dinner.
In the June Lake area next to the Oh Ridge campground is Pine Cliff resort off 395 at the South June Lake Loop. I've only used the showers since we always stay next door at Oh Ridge campground. Many of the sites there have sit down views of June Mtn. and June Lake but no hook ups. Friends of mine who have stayed there because they want hook ups have given it a good rating.
Hope this information helps,
in So Cal