Davenport is a slightly better bet weather-wise than Pigeon Point, as due to the shape of the coastline and prevailing winds the clouds usually get swept past it. But it still gets cloudy from time to time there. Route 1 in general is a toss-up.
If you live in South Bay, the hands-down best place IMO is Pinnacles National Park. It's only 1.5 hours from San Jose, and easily daytrippable.
If you don't want to go that far, try anywhere along the Airline Highway, in the Paicines or Tres Pinos area (just get away from streetlights; for example, Panoche Road is a very, very dark road), Coyote Lake (shoreline is open for stargazing 24 hours; pay with machine at entrance), Henry Coe State Park, or anywhere along Mines Road but at least 15km southeast of Livermore.
Also, if you're going for Milky Way viewing, do make sure you know when and where the Milky Way is visible. The bright part and galactic core are only visible very late at night now, after 11pm or so, in the east direction. In mid-Summer the MW will be in the sky all night. In autumn the MW will be in the southwestern skies early at night and not visible late at night.
At other times, such as in winter, the outer parts of the Milky Way are in the sky, but you need much, much darker skies to make anything of it, and it's hard to see without long exposure photography. The winter side of the galaxy is actually really beautiful if you do a long enough exposure and all the signal processing necessary to get rid of noise.