With absolutely no traffic, it is 1:40 from San Francisco airport to Monterey, 1:37 from Oakland, and 1:10 from San Jose.
But this is the bay area. "Absolutely no traffic" rarely happens.
In practice, rush hour traffic (in particular in the evening, when many people try to go home, to cheaper housing south of the bay area) will add roughly an hour to the trip from SFO or OAK, but less than 1/2 hour from San Jose. The trip from Oakland will be particularly gnarly, since the 880 and 680 in the east bay will be clogged in strange and unpredictable ways. Now you are comparing 2-1/2 hours to 1-1/2 hours. Why? Because San Jose is already pretty far south, and from there to Monterey you have two options (101 south to 156, or 17 south to Santa Cruz and then 1 along the coast), and even a detour via 87 and 85 if things clog on 101.
Specially beware of Saturday mornings and Sunday evenings, when everyone in the bay area tries to go to the coast and back. We call it "beach traffic".
By the way, Monterey does have an airport with regularly scheduled service. Flights might be a bit expensive.