Library
National Library
9 locals recommend,
Location
3 Arngrímsgata
Reykjavík, Reykjavíkurborg
Tips from locals
Lot´s of books, also serves as he university library. Reasonably priced canteen for coffe, lunch etc. Packed with students during School semesters, Frequent exhibitions on 1st floor.
If you need some peace and quiet free wi-fi to work. The library is quite nice. There i also a cafeteria here.