My favorite part of the park is the Washburn Point - Glacier Point area, where one can look straight down 3000' to the valley floor and look across to Half Dome. Near there, the trails to Sentinel Dome and Taft Point are excellent and do not have large altitude changes. The trail to Nevada Falls is supposed to be great as well, but I wouldn't know... my legs wore out about halfway up that steep climb.
If you're going to be east of the park, the woods are honeycombed with trails around Mammoth Lakes. For a fun and scenic drive up into the mountains (on rough pavement), head south toward Bishop and watch for the turnoff west through Rovana, and proceed to the end of the road. There are some dirt trails that climb westward also; have a look at a NF map for that area.
The photo in my signature was taken at Hetch Hetchy, in Yosemite.