According to Wikipedia, the original Globe Theatre in London could accommodate 3000 people and there were about 200,000 people living in London in 1600. So, ignoring tourists, the average Londoner could have visited the Globe more than once a week. And if memory serves, the Globe wasn't the only theatre.
Who would have had the time and money in Jacobean London for visiting the theatre that frequently? Do we have any idea how much of the audience would be idle aristocrats, versus the better-off merchants and clerks and skilled tradespeople taking an afternoon off work? Or passing sailors with money to burn?
Renaissance England had, generally speaking, two types of permanent theatre: enclosed (all seating) and open-air ("mosh pit" in the middle, likely with seating around the walls). While the indoor theatres tended to be much more expensive and have a more sedate crowd, open-air theatres indeed marketed themselves to the masses. Ticket prices were typically one penny, which was 1/10 of the average artisan's daily wage.
But one of the ways we know theatres really attracted everyone is the rather unsavory reputation that the open-air playhouses developed. They became rather infamous, for a time, as a target-rich environment for pickpockets and especially prostitutes to work. I just love the notion that the Elizabethan/Jacobean criminal underworld enjoyed the same cultural productions and were exposed to the same classical allusions and literary skill that are part of today's high culture.