prettybird, I wouldn't try Half Dome next -- the cables scares more people than any other place.
But for other peaks, you should climb White Mountain northeast of Bishop next. Then try Mt. Langley, just south of Mt. Whitney.
You didn't say whether you wanted suggestions for overnight or dayhikes, but White Mtn is a dayhike, while Langley is farther -- a Whitney-class dayhike, but a very nice overnighter.
Also, if you are in southern California, there are a number of peaks to try there.