The standard trip is to start at North Lake, go over Piute Pass, go southbound along the JMT, over Muir Pass and down to LeConte Canyon, then up over Bishop Pass and out to South Lake. I did that one a year ago, and it was very nice (assuming that you hit the season right).
You can sort of split it through the middle, using Lamarck Col. That would make it North Lake, Lamarck Col, Evolution, Muir Pass, LeConte, Bishop Pass, South Lake. In advance, you would want to know that you handle altitude OK. Lamarck Col is around 13,000 feet, so it will kick your butt if you are not prepared. For the next variation, do this on skis in April.
Another split is over Echo Col, but you would need to go clockwise around the loop.