Good pt, El Floppo...we had only touched on FiDi (less than optimal IMO), and Norwood had ruled out much of the rest - BPC is dreck, Tribeca/SoHo/GV-WV flat out ridiculous. But LES is an up and comer, East Village is just about the only authentic nabe left. I know you're right on the border of those two, and I have friends raising kids there...def more of a kid friendly nabe now than when you or I rolled into town.
Also, FWIW, it's $15K and $24K for freaking pre-k and friggin Kindergarden. You don't have to start paying $30K until first grade.
ETA: Chelseas/Flatiron seems a bit too expensive for the budget we're discussing, but there are plenty of blocks around the edge of Gramercy and MSP that would fit the range. But I'm biased, love downtown, can't wait to get out of midtown.