San Jose International is the closest major airport to Carmel. We recommend that over San Fransisco, but if flight times are better it only adds about 45 min to the drive down to Carmel.
Yes, unfortunately Carmel by the Sea is further south of the Bay Area. We recommend renting a car for the drive, but don't worry! You get to drive along scenic Highway 1 and can take a detour through Pebble Beach's famous 17 Mile Drive.
Carmel is charming and you can definitely spend time relaxing by the ocean and enjoying all the art it has to offer, but there are plenty of other local (and not so local) suggestions over in our "Things to Do" tab.
ASAP! We cannot stress this one enough - if you know you are attending (thank you!) please book lodging quickly. We have several recommendations over in our Travel page. Its a very busy time of year in Carmel and its a small beach town, so rooms will go quickly.