You are not going to find any guaranteed smoke free hiking anywhere near Yosemite for the next few days or maybe even weeks. They just announced that they have closed ALL roads into Yosemite from the West, so if you are flying into LA, you'll need to drive over to 395 and then North to even enter the park via Tioga Pass on the East side. Sorry that I can't give you better news. Things may improve in the next few days, but these fires are enormous and not going anywhere soon. The smoke does seem slightly less ubiquitous as you head North...
Alternatives? Since you are flying into LA, you could look at SEKI---but there is a fire that has stopped all trips out of Mineral King. The rest of the park is jam packed with people, from what I have heard--overflow from Yosemite.
You might try the John Muir Wilderness or Dinkey Lakes, or Jenny Lakes. Smoke there might not be so bad.
Further North, I would suggest looking at Desolation Wilderness to the West of Lake Tahoe. Beautiful area, lots of granite, lots of lakes, and far enough North that you might not have as much smoke (unless you get it from the Carr Fire up in Redding.) Between Yosemite and Tahoe, the Emigrant, Carson-Iceberg, and Mokelumne Wildernesses all offer some good hiking, Emigrant is closest to Yosemite, both in character and in location--and consequently in potentially smoke skies. Carson-Iceberg and Mokelumne are further North, and while they can offer some wonderful views, do not have the same geology---more volcanic, less granite, than Yosemite.
Last minute permits are probably easiest for Highway 108, which runs between Emigrant and Carson-Iceberg. And if you take 108 over Sonora Pass, you also have access to the Hoover Wilderness which also has great hiking. You can check out all of these destinations on our website, backpackthesierra.com.
If you get up towards Yosemite, you might find that the smoke is less on the East side...drive up 108 and watch the smoke. Stop in at the Summit Ranger Station near Pinecrest Lake and ask for advice, suggestions. If they tell you that all of their trails are still smoky, head up over the pass and check out Leavitt Meadows. Self-register permits at the trailhead for trips up the Walker River towards Tower Peak and Dorothy Lake---great area to explore. And if it is still smoky there, head north on 395 until the smoke stops, then turn West and see what you can find....
Another option is to go up Highway 80 or 50 towards Tahoe--but that's a long drive for you. Stop in at the USFS office in Nevada City (80) or Placerville (50) and ask for current permit and smoke conditions. If the news is bad, go past Tahoe and head South...and follow the same directions as above. There is USFS office in Bridgeport (East of 395 and South of 108) that can give you a good idea of what things are like on the East side.
All of these offices have phones, and will answer them---and answer you questions about current conditions.http://californiasmokeinfo.blogspot.com/
And this just in: Yosemite Valley is being evacuated...
From a post on Yosemite News and Discussion group by someone who is very familiar with the park and its staff:
"Convoys are meeting at El Cap Meadow at 1100am and 1200pm for Wawona exit. May also exit via Crane Flat to Tioga Pass only (this route is dependent on fire behavior and could close at any moment). Must leave the valley by 1200pm today."
Very sad news.