Hey there, in my opinion, the hike to Dusy Basin is a spectacular introduction to the magnificence of the Eastern Sierra. "ScottHiker" is probably right about the first few miles, although even the initial glance of the watershed from the South Lake parking lot is breathtaking. About 2.0 to 2.5 miles up the trail, you hit the beginning of Long Lake (if my memory serves me well) and the view from there begins to get much better. There are some great peaks to climb up there if you're ok with talus and some Class 2-3 scrambling, ie. Mt. Agassiz next to Bishop Pass. You can get quite a view of the Palisades and pretty much the entire range as far as you can see if you get up a little. Dusy Basin itself is an awesome place to spend a night or a few, but be sure to bring bear canisters as that was a very busy bear area in my experience.
Other great hikes out of Bishop include the hike up to Paiute Pass which is short and relatively easy but simply spectacular, especially when you get into Humprhey's Basin. I also love the Lamarck Col hike, also not to bad in terms of mileage and moderate to difficult. All these hikes showcase the rugged beauty of the Sierra, craggy spires, sparkling lakes and streams, and hopefully some solitude.
Have an awesome time.
