With just four days, I'd skip Sequoia & Kings Canyon; you'd end up spending a great deal of time just driving back and forth. There will be *plenty* to keep you busy for four days in Yosemite if you do some hiking; if you don't hike but just want to drive, you can do Kings Canyon one day.
Must-sees (in my humble opinion):
(1) Wander the trails and meadows of the valley, looking up.
(2) Drive to Glacier Point for the view (there are some fine hikes along the way, too, to Sentinel Dome and Taft Point).
(3) Hike the John Muir trail from the valley past Vernal Falls to Nevada falls.
(4) Tunnel View (the parking area outside the tunnel on the 41); to avoid the tourist hordes, take the trail that leaves from across the street up several switchbacks, and you'll get the same view without the hordes of people around you (the beginning is steep, however; wear good shoes).
(5) Drive the 120 into the high country, and hike to Cathedral Lakes (both of them). Overland it from Upper Cathedral Lake to the ridge overlooking Lower Cathedral Lake. (It's a sizeable drive; allow all day.) Stop at Olmstead Point for the view on the way there, and look for marmots there too (there are often some hanging around).
If you'd really like to see Seqouias, there are a couple of groves in Yosemite.
I'd go online to see if the park service has a park map available, so you can do some planning ahead of time.
However, Yosemite Valley is VERY crowded in summer. Be forewarned. Be patient and get in to get a parking space EARLY.
Where are you planning to stay? You're extremely unlikely to find anything available in the park at this point. Of the various towns outside the park, El Portal is the closest to the valley. However, there's been a lot of construction on the roads leading into the park from the west lately, with a lot of delays - check the park service web site and/or the Caltrans web site before making lodging reservations to avoid the roads with the worst delays.
Lisa