I agree with the Southern JMT recommendation. If you want a trail hike in the Sierra of ~100 miles, the southern leg of the JMT is the best choice.
I just finished a solo hike of ~110 miles on that stretch in 7 days. September in the Southern Sierra is perfect timing. I'm going back next week for another 9 days!
Here are key pieces of info about this route, probably more info than you want, but you don't have much time to plan so I thought I'd do a brain dump.
1. I went south to north, but the bulk of the hikers go N to S, so S to N means you see a lot more people since you are traveling against the grain. Also, if you plan to include Whitney, you want that at the end of your trip (if you follow rules) since in the Whitney zone you are required to bag and carry your human waste (they provide bags).
2. I parked in Bishop and took Eastern Sierra Transit Authority bus to Lone Pine (3 times a day for $5). In Bishop, stop at the police station and let them know you'll leave your car behind their station and they'll look after it for you! (if parking in Lone Pine I don't know where to leave the car.) Hitching from 395 to/from the main trailheads is very easy (I've always gotten rides from the first car that drove past).
3. At the southern end, you can access the JMT from Whitney Portal, or from the less chaotic entrance at Horseshoe Meadows (Cottonwood Pass or New Army Pass). If you can get a permit to Mt Whitney and you haven't been there yet, it's worth going once (beautiful, but very crowded). If you don't want to deal with Whitney, use the Horseshoe Meadows trailhead instead. Or, Shepard Pass trailhead would work, but it doesn't get as much use and hitching there from 395 might be more time consuming.
3. At the northern end, you can access the JMT from Piute Pass, Lamarck Col (fairly easy class 1-2 off trail), or Bishop Pass. Bishop Pass has the disadvantage that you would miss Muir Pass and the truly lovely area on the N side of that pass. If you are comfortable off trail navigating and dealing with some easy class-2 stuff, then Lamarck Col is the best choice in my opinion. Read the detailed info about the Col in Secor's guide (Peaks Passes and Trails).
4. This section includes all five high passes on the JMT (Muir, Mather, Pinchot, Glen, Forester) and the entire thing is fantastic. There are no crummy sections. I think Yosemite is a better choice for a 2 or 3 day trip, but there isn't a good long hike, and it's not as nice as the Southern Sierra (IMHO).
5. If you don't include Lamarck Col, then the only map you'll need is the 2 map set from USDA called "A Guide to the John Muir Wilderness and Sequoia-Kings Canyon Wilderness. Inyo and Sierra National Forests, Sequoia and Kings Canyon National Parks" It's a great map for trip planning in the Southern Sierra, and for trail hiking photo-copies of the appropriate sections are all you need. Here's one vendor:
Good luck, Amy