OK, I have a slightly different approach, only because you are acting as if you are going to be able to camp in Yosemite Valley...and those campsites are all gone, and have been gone for weeks. So while I totally agree with the others here about what you should see, you need a plan for a place to sleep!
You don't mention it, but I am assuming that you have a car, and that will make things a lot easier.
1. When you arrive, go directly to the wilderness office (there's one in the Valley, but if you come in one 120 through Big Oak Flat, the best way from SF, there is one at the entrance station.) Stop there and get a backpacking permit for the next day. Unless you arrive at dawn, most of the permits for the really popular trails, like Happy Isles, Cathedral Lakes, etc. will be gone. That's OK. There are always a few places that don't seem to be on most people's radar, because they don't take you immediately to the most popular destinations. I would suggest that you get a permit for Murphy Creek, at the East end of Tenaya Lake, with your destination being Polly Dome Lakes. These are small lakes with no fish, about 2.5 or 3 miles in from the road. They are perfectly pleasant, and it's a nice hike with only a very short cross-country use trail to get to them.
Once you have your backpacking permit, you now get to spend one night before your backpacking trip in the backpacker's campground, either in Yosemite Valley or Tuolumne Meadows. Because Polly Dome Lakes is a short hike, you can spend the rest of the afternoon and the next morning exploring the best parts of Yosemite Valley, for example, and still have time to hike to Polly Dome Lakes, even if you start at 2 or even 4 p.m. from the trailhead.
And the next morning, you can rise, hike out, and explore more of the park. And because of that wilderness permit, you're allowed one more night in one of the backpacker's campgrounds following you trip. So with one simple permit, you get three nights in Yosemite. And you have plenty of time to see what is so wonderful.
My favorites? GLacier Point, with a hike to Sentinel Dome and Taft Point. The shuttle around the Valley, getting off wherever things look good, and poking around---particularly out in the meadows of the Valley itself. It's amazing how few people hike the trails into the meadows, and how alone you can feel in the middle of the park out there. In Tuolumne Meadows, climb Pothole Dome for amazing views. And from Tioga Pass, hike up over the ridge to Gaylor Lakes. Stunning.
And just for fun, here's a photo of Polly Dome Lakes...and a link to our hike there a few years ago:
https://picasaweb.google.com/balzaccom/ ... ayHikes09#And a link to more hikes in the fall...
https://picasaweb.google.com/balzaccom/ ... yHikes2010https://picasaweb.google.com/balzaccom/ ... yHikes2014