There's one right near me http://www.shaloh.org/
I'm not sure it's that cheap though. If it was, I'd probably send there.
As I said, there are a few. One recently opened in Brooklyn Heights (and for some odd reason advertised also in Crown Heights).
There's also a school in Crown Heights that many would consider of that type.
As I said, there are a few out there, but it's a tiny percentage of the overall reach of Chabad Lubavitch in the US.
There are quite a few people in the Lubavitch community who joined the community because in the 1950s and 1960s United Lubavitcher Yeshiva was the only Jewish school which would accept every Jewish child, regardless of ability to pay tuition. There are also many that attended that didn't join the community, but appreciate the fact that their parents were able to give them a Jewish education thanks to the policies and hard work the fundraisers did. Same can be said about the origins of Camp Gan Yisroel.