I have a cousin who lives in Los Angeles and was visiting New York. He was staying with his other relatives in Canarsie section of Brooklyn. When I came over to see him we went out for some pizza. As we crossed the street he turned towards a Pizza Hut and I was like "Dude, where do you think you're going? Any corner pizza joint here is better than Pizza the Hutt." (Spaceballs reference.)
Anyway, there are 2.5 million people living in Brooklyn; if you ask them about the best pizza place, you will get 5 million opinions. While Grimaldi's does serve great pizza, it has become something of a tourist trap with prices to match and long waits for a table. It is right under the Brooklyn Bridge and most tourists don't venture further afield. Of trivial note, an English pop group Bananarama shot the video for its 1983 hit It's a Cruel Summer on that block.
Try Totonno's on Neptune Avenue and West 16th Street. The place has been there since 1924! Take any train that goes to the Coney Island - Stillwell Avenue Station, exit toward Mermaid Avenue, walk north on Stillwell to Neptune and turn left. Check the hours of operation, the place is not open every day.
Also, try a couple of corner slices of Grandma's or Sicilian pizza (or one of each) and then some spumoni at L&B Spumoni Gardens, another old fashioned pizza and ice cream place, on 86th Street and West 10th Street. Take the N train to 86th Street Station.