We will be spending the night of our arrival and departure near the airport, but are wondering about transportation to downtown Convention Center. Do not wish to drive in the city.

http://www.flysfo.com/web/page/tofrom/transp-serv/

Many SFO hotels have shuttles to either BART Millbrae Station, which you can take to Montgomery station--the stop for Moscone convention center, or to SFO where there is a BART station

Your choices are taxi (about $40), shuttle ($17 per person) or BART (subway). Like SAB, I would recommend BART. FWIW, the BART trip is much more expensive from the airport ($8.10 per person one way) than from Millbrae ($4.25 per person one way).

BART is perfect for going to the Convention Center.

In my experience the hotel shuttles to/from the airport are a royal pain to try to connect into SF. You can burn a lot of time waiting for the shuttle at the hotel, relatively quick ride to the airport, then again waiting for bart. Ditto on the reverse back to your hotel. Not all the airport area hotels have shuttles to BART Millbrae station, or they may be infrequent.

To me the best of both worlds is getting a hotel near the Millbrae BART station. There is a Fairfield Inn within close walking distance. I've not stayed there, but I use other Fairfield's a lot and they are consistently clean and comfortable.