If you take highway 101 from Monterey to Santa Barbara, it is probably about 4 hours - no need to stop overnight on the way. If you do go this way, I recommend a "short cut" - at exit 146 south of Santa Maria and just north of Buellton, take highway 154 to Santa Barbara. It goes through the town of Los Olivos, the center of the Santa Ynez wine country, past Lake Cachuma and some great scenery. Even though it is not a freeway, it is much shorter than 101 and takes the same amount of time. Or you could take the next exit at Buellton (exit 140A - highway 246) and go east on 246 to the Danish town of Solvang (definitely worth a lunch stop) and pick up highway 154 just east of Santa Ynez.
On the other hand, if you take the coast road (highway 1) south from Monterey, it will take at least 2 hours longer and you may want to stop overnight in Cambria or Morro Bay. Be advised that for a good stretch of highway 1, it runs along the side of the cliffs (beautiful scenery) but the road is quite winding and you are driving on the ocean side of the highway. Some people are not comfortable with this drive, although it really is quite safe.