I also live in San Jose. This is what we did. We woke up early the day before the hike, we drove to Lone Pine, went to get our permit and then drove to the portal.

***We didn't do this but next time we will***
Do a small hike up to Lone Pine lake. Go back down, maybe rent a bed at the Lone Pine Hostel (only $25 for a bed and $5 for a shower). Wake up super early on the day of the hike, summit, head back down, sleep and go back to San Jo.

Instead of taking 120, we went the other way. 101, 152, 5, 58, 178, 14 and 395. We saved an hour of driving and the $20 dollar fee at Yosemite.