It has always been the case that parents in northwest Brooklyn have looked to lower Manhattan and the east side as possible options when their neighborhood schools didn't serve. Recently the old elementary standbys like the Earth School have not been able to take students from outside their districts much less their boroughs.
District 2 has long been the Holy Grail of progressive education but aside from I.C.E. it is closed to outside middle or high school students.
When the DOE announced that there were new schools opening in lower Manhattan to help ease the overcrowding there, I inquired about whether there might be a spot or two open for Brooklyn families in either PS/IS 397 The Spruce St. School or PS/IS 276. The report was not encouraging. The projections show that they are probably already over capacity. It never hurts to inquire, but don't count on finding a placement.
There was better news at the Manhattan Charter School, the only K-5 charter below Houston. They give priority to District 1 students but they often move onto their waiting list as many charters do. A significant percentage of current students are from Brooklyn and the school is very convenient to the F train - a couple blocks from the Delancy St. stop. This school which has been open for 6 years has had a rocky beginning with a total of 3 principals since its founding, but the current principal, Genie Depolo, seems to be there to stay and the classrooms are bright and focused. They are particularly interesting for their French and music enrichments. Definitely worth a tour.