There are some fields in Manhattan. Games are played in all 5
buroughs. I think there's some PSAL guys on this website. Here's the website for the PSAL Football Officials Association:
www.psalfoa.orgI think the city pays $108 for Varsity. Not sure about youth.
NY metro area football games are shown on local channels. So you won't see them on the Fox Affiliate or something like that. You'll see them on "MSG Varsity" or "Verizon 1." Those channels are dedicated to HS sports and do a decent job.
Football is pretty big on the island and surrounding area, but the city and Long Island do not participate in the state tournament. PSAL uses 4 man crews as do some other parts of NY state. I think PSAL has a lot of varsity games on Sunday. Other areas are mostly Saturday with some Friday nights.
Soccer and Lacrosse are popular as well. Lacrosse is increasing in popularity. I don't think NY will ever have spring football because it would take too many kids away from Lacrosse, Track, etc.