This page is mostly about parking near airports around NYC. Spot Hero app is also a great resource to check for affordable parking.
Spot Angels app will show you where there are street cleaning routes in NYC, and where there aren't.
LGA
If you have a car, you can park for free for 1-2 weeks in or around Rego park and then take a fifteen minute Uber or the subway to LGA.
JFK
Air Train is a free way to travel between terminals and outside the JFK airport.
You can park for free about a 10 min walk north of Lefferts Blvd airtrain station. Around 118th St and 150th Ave. There's no street cleaning there, so you can theoretically leave a car a couple of weeks (I have left a car there for 2 weeks at a time without issues).
EWR
Cheap long-term parking new EWR Newark Airport with a free shuttle:
https://www.victoriaairportparking.com/
Alternatively, you can find street parking in Elizabeth, NJ, and then take a quick bus ride (bus #62) directly to the EWR terminals.