that's why I asked how many miles you were interested in doing.
you could do anything from a very casual 30, to a somewhat intense 160.
a very nice and logistically easy trip is Mammoth/Reds Meadow to Tuolumne or Yosemite Valley. could be from 30 to 57 miles depending on start/finish.
a nice big bus will take you back to the start cheaply and fast (YARTS).
permits are easy at the Mammoth end for walk-ins, a bit harder at the Yosemite end.
the country is some of the JMT's best.
and Yosemite adds in other options to the trip if you have never been there.
so a lot of this depends how alone you want to be also, since Tuolumne and Yose Valley are not exactly empty of people in summer.
A longer (but with fewer people) option is Onion Valley/Kearsarge Pass to Reds Meadow/Mammoth.
125 miles, sections over the big passes can be fairly remote even in summer. you finish at a nice ski resort town to get a bit of civilization when its done.
travel logistics are a bit more involved but easily doable.
p.s.
my 2 least favorite sections are :
1. from Whitney Summit down into Crabtree, Tyndall, to just before Forrester Pass.
yes it is nice here, but other areas are even better.
2. Cathedral Peak to Yosemite Valley
again nice here, but a bit crowded in summer, relatively speaking, and I prefer the high country.
there are no bad sections.