If you're going to do half of the JMT I'd recommend the south half. Bigger mountains, less walking through western slope forest. And there are more and better side-trip options available. A few ideas for side trips for the north half would be climbing Half Dome/Clouds Rest, detouring to the Washburn Lake area, and visiting Ediza/Minaret Lakes. If you're an experienced climber, consider Mount Lyell (class 3) while you're there - it's the highest peak in Yosemite.
I'd also recommend the SHR section from Red's Meadow to Duck Lake, it's much more interesting than the JMT. It's also pretty straightforward in terms of routefinding once you find the correct way from Mammoth Pass to the crest.