You can get to Queens Central Library by bus or train. The 169th St on the F train is very close. There are many buses that stop nearby and there is a bus depot across the street.
Check in the library website. After click in Hours and Locations. Once there, select the branch that you like to visit. Once there, check the right side, and you will see a box named DIRECTIONS. you will get info about Bus, train, car and a map.
By bus or train depends where are you coming from. Also there might be a closer brunch at your place.
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