When my wife and I had our first child, we lived in SF. The neighborhood daycare in the Excelsior charged $1600/mo. This is five years ago. We're about to have our fourth child. With the upcoming summer, if we still lived in SF, we'd have four children in daycare. $6,400/mo.
Anyone living in a high COL city with multiple kids should look into importing an au pair. $2k a month would really help the au pair and her family back home and save the family potentially hundreds of dollars a month
The minimum wage for NYC is $15 an hour and ultimately if you pay the minimum you get your pick of the worst employees.