There is a very small long-term parking lot between Terminal B and Terminal C at La Guardia. The first 48 hours run $24.00 per 24 hour period, $5.00 for every 12 hour period after 48 hours.
Across from the airport there is privately owned lots:
AirPark $20.00 per day 718-898-8400
National $19.00 per day/ 8th day free 718-429-5893
Clarion $13.00 per day/ 8th day free 718-335-6713
Call ahead to insure a spot in the lot.
Hope this info helps.