Plenty of school districts in New Jersey have allowed tuition students for years. I sent my daughter to a neighboring public school as a tuition student for the first half of her first grade year, until I could get her in a charter school as a midyear transfer. Prices vary greatly, as does the willingness of school districts to take students (space permitting, of course). As an odd side note, River Dell High School is fed by Oradell and River Edge. Oddly, the former town does not accept tuition students, but the latter does, and is one of the elementary school districts we considered paying for. Most around us were anywhere from $8,000 to double that.
Of course the choice program is an entirely different story.