Some hikers tend to be more interested in moving as far along their trail routes as possible each day regardless of where they end up. Wherever they stop and camp, they tend to stay near camp vegging without further activities so if it is only early afternoon they may become bored. Others are more interesting in ending up in most scenic locations even if that means they might stop at some places mid day. And they might be fishermen, peak baggers, or photographers interested in an activity.
From the Onion Valley trailhead I would expect given your fitness, you could easily get over Kearsarge Pass and ramble down to Vidette Meadow about 10 miles. That is down in a deep forested canyon with good campsites abundant along the big through trails and a favorite area of black bears. Views down in such canyons tend to be limited. If your first day has thunderstorms, this would be a more pleasant goal than up near the crest.
The most scenic place to stop and camp with outstanding sunset light would be near the outlet of Kearsarge Lake 3321 that is at the cross hairs of this online map:http://mapper.acme.com/?ll=36.76650,-118.38995&z=15&t=T
The Kearsarge Pinnacles and University Peak are spectacular from that area. Then again in the morning the former is wonderful reflecting in the usually calm of early mornings. Those lakes also have an abundance of pan sized eastern brook trout. There is also some value in not making the first day too stressful especially since your bodies will be at these high elevations for the first time that may require some acclimation. Most groups camp close to the trail at the second lake to the northeast with the location I noted more secluded with better views.
From the noted 3321 spot one can simply descend along the stream and catch the trail above spectacular Bullfrog Lake as the terrain is quite open. Then if hiking from mid morning the second day one will probably want a goal of either ending up on either side of Forester Pass. Neither with interesting sunset light. The south side is more austere with several large no name lakes. In the Sierra mornings are often calm till about 10am then breezes start and by afternoon it can be windy and stay so till evening. The winds go up canyons during the day and the broad south side plane below Forester is a natural wind tunnel. Most thru trail hikers tend to camp right along side trails. The little pond at these cross hairs is far enough off the trail that it is likely to be secluded. It is 9 or 10 miles along at the highest timberline with anything higher barren turf, rock, and snow landscapes. Fine views of Mt Stanford early morning.http://mapper.acme.com/?ll=36.71734,-118.36881&z=15&t=T
Stopping north of the pass you could get on the trail early the third day and quickly get over Forester Pass when fresh. From there the trail is very easy low gradient downhill walking. For a destination another 9 or 10 miles along will suggest camping near the small pond southwest of Tawny Point that is called Bighorn Plateau. http://mapper.acme.com/?ll=36.61883,-118.38163&z=14&t=T
Most groups will continue down into the mosquitoey meadows along Wrights Creek where views are somewhat limited though has abundant pan sized stream trout. For a late afternoon activity, one might make the easy climb northeast up to Tawny Point or wander off southwest to the end of the plateau that has spectacular foxtail pines to frame Mt Whitney zone peaks near sunset. And in the morning are more fine views west to the Great Western Divide peaks.
Then on day 4 reaching Guitar Lake and Trail Crest is rather straightforward through superb timberline scenery leaving a final day of downhill to the Whitney Trailhead.
The most ideal dates for the High Sierra most years tend to be mid July through early August. The annual mosquito plague usually peaks late June to early July and then quickly wanes except in swampy meadow areas. Popular trail crossing shady north facing snowy areas by early July usually have well pounded boot paths through without a need for special gear.
Davidhttp://www.davidsenesac.com/2015_Trip_C ... les-0.html