The best airport to fly into is San Jose International (SJC). Failing that, either San Fransisco (SFO) or Oakland (OAK) can also work.
Since this is California, the best way to get around is likely to rent a car or (preferably) carpool. Car rentals are available at all the airports, as well as other ground trasport options (for example, from San Jose). It is possble to take the Santa Cruz Airporter bus from SJC for about $40, they can be reached at 800-497-4997.
The drive time from the south bay to Chaminade is about an hour in moderate traffic. Add about a half hour if you are arriving into SFO or an hour if you are arriving into Oakland. You should also be aware that the best route to Santa Cruz from the bay area (Highway 17) is a somewhat winding mountain pass road that locals tend to drive relatively quickly when traffic allows.