Regulars on the board can see this coming, but the
Mt. Ritter and Banner Peak area is my particular favorite. (Hey, the mountain has my name on it, can you blame me???)
Seriously...from Agnew Meadows to Ediza Lake is about 8 miles. The scenery, especially around Shadow Lake and once you get up to Ediza, is drop-dead gorgeous. It isn't called the Ansel Adams Wilderness for nothing! The Mt. Ritter section of my web page has shots from several of our trips up there.
If you want to climb "my" mountain check out the route description in the '99 Mt. Ritter trip report. Ice axe and crampons are required but it's quite doable. Even if you don't climb and just hike into Ediza for a couple of days, it's worth the trip.
For a longer hike (10 miles each way), you can go up the High Trail (PCT) to Thousand Island Lake and see the other side of Banner and a little bit of Mt. Ritter peeking over his shorter brother. Then hike back via the River Trail (along the San Joaquin) for a different return path with a lot of pretty rapids and short falls.
You might guess a certain bias here...guilty as charged, Your Honor.