Anyone who loves fresh made mozzarella should make a trip to Lioni's in Bensonhurst (15th Ave and 78th Street). My uncle has been going there for years. The mozzarella is made fresh throughout the day. It is sold in pound pieces 3/$10. Boccocini are also available for $2 a pint. The BEST price ever for fresh mozzarella. I've gotten it plenty of times when it's still warm. It's available salted & unsalted. The other great thing about Lioni's is that they are the only outlet I know of that will sell fresh curd if you want to make your own fresh mozzarella. A lot of cheese markets just won't sell it.
Of course they sell more than mozzarella, so make a trip soon. When you visit, make your way to 13th Ave ans stop by Mona Lisa's on 13th and 78th for drop dead prosciutto bread as well great Italian and Frech bread.
The best way to get there by train is take the B train to the 79th Street station. You'll have to walk about three blocks.
My other favs are Cangiano's on 3rd Ave and 70th Street in Bay Ridge, and believe it or not MET Food on Henry Street and DeGraw in Cobble Hill.