Only rappers say "Frisco" any more, probably because it's easy to rhyme. The most common abbreviation I hear is simply "SF" for San Francisco itself. "East Bay" for Oakland, Alameda, Berkeley. etc. "The Peninsula" or "The Valley" for anywhere south of SF and "Bay Area" for the whole thing.
I also hear "The City" for San Francisco often enough to find myself using it on occasion (Something I vowed I'd never do after bristling at my friends using the appellation for NYC when I lived in the Northeast).