Unless you're really strapped for space, I'd bring the crashpad if you're into bouldering. Castle Rock State Park, Indian and Mortar Rock in Berkeley, Vacaville/Nut Tree, Goat Rocks, etc., etc.. There's much more bouldering than sport climbing within the ~1 hour range. You have to drive more in the 2+ hour range to get to the sort of sport climbing you'd be into.
I would say keep it unless you are really, really tight for space. You will quickly exhaust all local climbing options (sport, bouldering, and otherwise) and need to travel several hours in a car to get to the destination areas, where there is plenty of world class bouldering.
Bring it. Being based in Palo Alto, you're going to spend a lot of time in Castle Rock State Park. It has some short roped climbing but the bouldering is better and more plentiful. If you're not at castle rock you'll probably be driving 3+ hours to Tahoe or Yosemite.