How long did famous pirates like Blackbeard really spend at sea?

Sorry, I would have responded earlier, but it's that time of the year when holidays (and whatever sickness it is that is passing around) are kind of a distraction.
TL;DR = Really hard to come up with a "average" because there was so much variance between pirates - even in the GAOP of 1713-1725. A voyage could be a few days to many months.

It all depends on the crew, the region, and the area. There were some pirates that operated out of small-ish boats (called periaugers) from 1713-1716 from the Bahamas - those trips would have been only a few weeks (might be easier to count it in days). Then, you had some crews that had vessels and sailed around the Caribbean and North American coast for a few months before returning to a base such as the Bahamas (depending on amount of prizes taken). Then, after 1718 when the Bahamas base was taken by by Woodes Rogers and British authority, pirates often had no choice but to keep to sea a lot of the times. Mind you, pirates (and ships in general) frequently had to touch land for picking up essentials (like water and food if for some reason a pirate crew wasn't finding enough prizes, which could happen depending on the time of year and location) or to do repairs (such as careening where the ship had to be brought up on the beach to scrape the bottom of marine growth that could slow a vessel's speed). Pirates did try to make bases (temporary or otherwise) out of other places - such as Blackbeard trying to set up a kind of place of operation out of North Carolina, and Charles Bellamy raided a small island-town that couldn't defend itself (due to lack of weapons and small population) in the Lesser Antilles of the Caribbean and kind of took advantage of that town for some days. On the African coast, there was a sort of base at Sierra Leone for a while, and pirates tried to trade and do other things along villages on the African coast (which sometimes ended poorly as is the case with Captain Edward England's crew that had to fight a whole African village because of them messing with their women). Especially after 1718, a kind of system of sailing around the Atlantic did somewhat develop, sailing between Africa, the Caribbean, the eastern North American coast, and back. The pirate base at Madagascar was kind of revived in the 1720s when some pirates went for the Red Sea again instead of back to the Caribbean. As for how long pirates spent on land - again it varied (where were they, what were they doing, if it was for pleasure how stuff/money did they have, etc.). But, based on Marcus Rediker's survey of about 900 individual pirates, spending 2 years overall as a pirate before disappearing, death in battle, or capture and execution seemed to be typical (though plenty of pirates spent much more or much less time than that as pirates too).

You can get a lot of this history from such books as Colin Woodard's Republic of Pirates, Benerson Little's Sea Rover's Practice, and from Marcus Rediker's Villains of All Nations.