This is one long drive. Like really long. It'll take about 2-2.5 hours end to end. Wear sun screen as you will get sunburned on the way up or down. There isn't a lot of shade on the road. If starting at Livemore the road begins as a single lane. After about 45 mins or so, the road narrows down to the point where there is only a single lane in both directions. There is enough room for a BRZ or an S2k to share the road with an F-250, but that's about it. Once you hit the mountain itself the road turns to gravel. Based on the construction equipment left around it seems that CalTrans is in the process of repaving it. The surface is slippery. Once you get closer to the top the road becomes paved again. Rather nicely I might add.
Once up top, Lick Observatory is a pretty cool place to check out. A lot history in the place. Be sure to check out the tour if you are up there. There is a vending machine, post office and a gift shop up there. Its a good place to rest up before heading down.
Heading back down towards East San Jose is a pretty nice run. The road has been recently paved, and has some amazing views of San Jose on the way down. The corners are pretty tight, barely wide enough for a BRZ. Visibility is bad as well due to the tightness of the turns. On coming traffic may move out into your lane as they are navigating up to the Observatory, so watch out. Eventually you'll end up in the foothills of San Jose and get dumped out into a residential area. 680 is another 15 minutes or so away.
All told, worth the drive, but its a bit of a mission. Most definitely a day trip.