Well, for easy access, nice scenery, JMT, and high(ish) elevation the best place by far with all those features is Lyell valley. Might be a bit crowded close to the road in August, but once you get past the day hikers should be OK. Its about 11 miles or virtually flat walking up a beautiful valley with a beautiful river surrounded by mountains. Mt. Lyell (or at least the general area), the highest peak in Yosemite will be visible at the head of the Canyon after 4 or 5 miles. Its one of the longest, if not the longest, flat stretches in the sierra. Permits however, might be an issue. Have to do a walk up.
If this is the first time your friend has gone backpacking post-injury I think this might be the ticket - the least likely route to cause him to want to turn back early. Let him get something like this under his bet first, and maybe he will actually want to go again.
You could squeeze and very leisurely 4 day 3 nigh trip out of this based on the mileage you mention going up the valley and then back. You could do some fishing and/or lounging by the river to fill in the time, and when you reach the part at the end of the valley, depending on how he is doing, you could go up as far as you want. Even if you don't go to the top there are some nice views of the valley and some camping spots up there.
Should be lots of other suggestion, maybe one less of a permit issue. Good luck.
Edit: David's and my posts passed in the ether.