If you want in Yosemite but not valley, Clouds Rest is a good long day hike. Though I assume you'll go past it on your trip. North Dome is a very nice easier day hike.
Outside of the park (east side):
Best scenery for least effort (if you're dead tired) is Little Lakes Valley off Rock Creek Rd.
Haven't done it myself yet, but the Mammoth Crest loop from Lake George looks like it'll be amazing.
If you're backpacking for that night you could do a real nice one-night trip to Thousand Island Lake from Agnew Meadows. Or if you have a car shuttle do a through hike from Agnew Meadows to Rush Creek/Silver Lake via Thousand Island Lake.
Or backpack up McGee Creek to Big or Little McGee Lake.
Pretty much everything off CA-168 from Bishop is awesome, but that's kind of far from Yosemite.
If you want specific campground recommendations just ask as I know all the campgrounds on the Eastern Sierra like the back of my hand.
Hi Sukhoi - I was hoping you would show up.
The plan is as follows, over 7-8 days:
-take the shuttle to Lake Tenaya, head west on the Sunrise Lakes trail
-Cloud's Rest, then Half Dome; do the cables
-west to Vernal & Nevada falls
-west to Clark Point, then west to Illilouette Falls
-west to Glacier Point, short detour to Sentinel Dome
-west to Taft Point, then Dewey Point, then Inspiration Point
-come out at Tunnel View parking lot.
-hitchhike to Old Big Oak Flat Road trailhead on the north side of the valley
-east to top of El Cap
-continue east to Eagle Peak, Upper Yosemite Falls, Yosemite Point, then North Dome
-backtrack west a wee little bit and descend into the valley on the Upper Y. Falls trail
So there's very little in & around the main valley that we won't hit. That's the reason we want to burn our last "extra" day outside the valley. Hetch Hetchy is kind of tempting...