Ilha do Mosqueiro is about 40 miles from Belém and can be reached via the BR-316 and the PA-391 highways and finally by crossing the Sebastião Oliveira bridge. By car, it’s no more than an hour away and buses leave Belém daily to the island (with a comparable arrival time). To get an idea of where it is, check out these maps on the official site.
Altogether, there are 16 beaches and in the month of July, around 300,000 people from all over Brazil visit the island for its non-salty waters and summer parties. The original holiday-goers were foreigners which, while taking advantage of the Rubber Boom at the end of the 19th century, found value in the island and started to build summer mansions there.
Judging by the photo up top, if you want peace and quiet, Praia do Farol is not what you are looking for, so try the maps to see where other beaches are on the island. I’ll leave you with a little piece of the peaceful part.
(the original song is from Jorge Drexler, called La Edad del Cielo)