Patrick,
Great question! Here are the places where you can drive up and camp NEAR the JMT. These are also popular resupply points, so you’ll probably use one of more them anyway.
Tuolumne Meadows – Yeah, if you’re starting from Yosemite Valley you’ll likely reach this on your third day, but take advantage of it.
Reds Meadow – On the backside of Mammoth Lakes lies Reds Meadow. There is a campground in this valley near Devil’s Postpile National Momument, but they will need reservations. Otherwise they will have to ride the shuttle in from Mammoth.
Vermillion Valley Resort (VVR) – This can be accessed from the west side of the sierras at Lake Thomas Edison. The big problem here is that you have to travel quite a ways off the JMT to reach this. In normal rainfall years, there is a ferry that you can take from one end of the lake to the other (well worth it IMO), but right now that lake is very dry and very low. Unless things change dramatically this spring, don’t count on the ferry. Still, this is an option.
Muir Trail Ranch – This is another popular resupply point, but it is not driveable. They would have to hike in to reach this spot. Some friends of mine did this on my first JMT trek.
That’s it. Not a lot of options. On the bright side, that means you’re in some pretty amazing wilderness (i.e. no roads). Have a great hike, and let me know if you have more questions.