Dublin is very close to Livermore.

We're in Mountain House which is east of Livermore.
Livermore, Dublin, and Pleasanton are all in basically the same area.

San Ramon is really close as well and I've heard good things about the schools there so it might be worth checking that area out as well.

The charter school in Tracy is supposed to be good but has a long waiting list so I assume the one in Livermore may be similar on a long waiting list.