|Courtesy: Long Beach Shakespeare Company|
One of Shakespeare's contemporaries in London was a sword master named George Silver. Silver was noted as a master teacher but in addition to the sword, he was also fond of the quarterstaff. By Shakespeare's time, fencing was a sport and no longer the deadly martial art it had been in previous centuries when it was used to settle judicial quarrels and all the fights were to the death.
There are a lot of places that teach fencing and stage combat but it's harder to find schools that specialize in historical western martial arts. In the Los Angeles area, there's the Academy of Arms.