Look here first:
http://www.nps.gov/yose/planyourvisit/upload/fulltrailheads.pdf
Be sure you page through to find the trailheads you are interested in. If you find the date or dates you are interested in for the trailhead on this list it is filled up, and there is no point in sending in a fax for that trailhead and that date. You can try to get one at the last moment in person, but no guarantee.
Since you did not mention dates (the most important thing by far), I am assuming this is a bit new for you. Yosemite starts taking reservation many months in advance – to be precise 128 days in advance. The most popular trailheads fill up nearly on the first day it is legal to apply (128 day before!), and on the worst of them, like Happy Isles and Lyell valley they even need to do a lottery the FIRST day it is legal.
For example if you sent your fax tonight you could apply for trailhead opening up for reservations on September 20. You will see that for Lyell Valley ALL the days in July, August and up to September 10 are full NOW.
Anyway, check to make sure the trailheads you are applying for are not at the very least already taken. The quotas are only for the starting points. The exit point are not that important. But yes the starting trailhead/fist night camp area DOES have to be exact.
If you use a map and the list of already closed trailheads to eliminate option you should be able to pick one that will work for you, you just may not be able to camp the first night in Lyell valley in August. The are sneaky but legal ways around full trailheads.
If you want more specific suggestion you really need to tell us where you want to go, and one what date. Maybe some people can suggest alternate trailheads and routes to get you there. For example if you want to go over Donohue pass then you could start from any available trailhead south of hy120 and route over into the lyell valley. Rafferty toward Vogelsang, and then over Toulumne pass to Lyell is one that come to mind, but just check at that one is also booked solid.
Mono starts look like you best (maybe only) bet – somehow below the radar. But check for your date, as even a few dates are full for starting there. I would take Lyell off the list since there is no point unless you are planning to go late in the season.
BTW id you really did mean to go in late September you don't even need reservations at all.