I'd like to make the argument for Death Valley. But before I get into that--after Yosemite, make sure you hit up Manzanar. It's no trail run, but it's literally on the side of the highway as you drive down South and it's one of the most eerie and fascinating outdoor parks I've been to. Takes about an hour to check out everything.

http://www.nps.gov/manz/
San Francisco, CA to Manzanar NHS (~338 miles) - through Yosemite National Park Take I-80 east towards Oakland for 7 miles. Take I-580 east towards Hayward/Stockton for 46 miles. Continue on I-205 east towards Stockton/Tracy for 13.5 miles. Take I-5 north for 2 miles. Take CA-120 exit towards Manteca/Sonora for 6 miles. Take CA-99 north for 1.5 miles. Exit on Yosemite Ave/CA-120. Turn on Yosemite Ave which becomes CA-120. Continue on Yosemite Ave for 11 miles. Continue on CA-120 for 143.5 miles. Turn on US-395 south for 110 miles. Manzanar is on the west side of US-395, 5 miles south of Independence, CA. Note: US-120 is closed in winter and spring. Use Highway 88, US-50, or I-80.

Now for the argument--the best trail run I've ever done ANYWHERE is Telescope Peak in Death Valley, not far from where you'll be heading. At 11,300 feet, it's the highest peak in CA and from the trail you'll be able to view Badwater--the lowest point in the western hemisphere. Telescope Peak also has one of the greatest vertical rises above local terrain of any mountain in the contiguous United States (don't worry, the grade from 8k to 11k feet isn't all that bad). Ancient Bristlecone pines dot the singletrack and it's too high up for reptiles, so you won't have to worry about stepping on a rattlesnake and dying alone up there. Round trip it's 14 miles and you can run almost the entire trail (the last part you do some scrambling with your hands up stepped rocks). And even though it's summer (and prob. 115 on the desert floor), the weather up at 8,000 feet will be perfect (70s) and you won't need a 4x4 to get up to Mahogany flat this time of year. If you're feeling really brave, you can run through Golden Canyon, hike down the Ubehebe Crater (3 min, down, 30 up!) or do a three mile out and back from Badwater in the heat to get an idea what the Badwater Ultra feels like.

As for King's Canyon and the Sequoias....first time I went I allocated a day and ended up only staying for a few hours--the trees are amazing, but after a while I was pretty bored and I missed Death Valley.

In "the Valley" Run from Happy Isles to the top of Half Dome. Killer! Take a camel back or some such and snacks...start early...watch for bear.

Happy Isles to Half Dome...would definitely be a killer. I saw a guy running by Crabtree Meadows (west side of Whitney) while I was hiking..this was at about 10,000ft, apparently he must have been camping somewhere and had a creek to clean up in after the run...he was all by himself. You could always run up to Mt Whitney on the regular trail...be careful coming down, though, cuz that's what will get ya. Blackbears in Yosemite generally won't kill you, but they'll scrap with you to get any food. Or check out a section from Cottonwood Meadows trailhead SW of Lone Pine...you could run over to New Army Pass, and that would be a long, hard run (I don't remember the mileage, but defnitely around 20 or more), and you can make it a loop.

In Zion, you could run up to Angels Rest and beyond to some point on the West Rim Trail. After a flat section just beyond Angels Rest, it gets pretty steep for a few miles and should be a beautiful, great workout. In the NW section of the park, you can run about 8 miles one-way to the largest arch in the U.S. that sits near a beautiful creek area (easy access to I-15 for this one!). Take lots of water on that one cuz there isn't anything between the start and finish.

One good thing about hiking alot, you start thinking about which ones could be trail runs.