These deals come and go over time, so I thought that I’d summarize the current offers.
National offers a 12-hour one-way rental between EWR and either Manhattan or Jersey City for $9.99+tax. Gas is
not included, but there does not seem to be a cap on mileage. Offer is valid in both directions, but on different days of the week, depending on direction of travel. Details here:
https://www.nationalcar.com/en/car-r...k-one-way.html
Avis and Budget offer a $9.99+tax rate for a 12-hour rental between some Brooklyn locations and LGA/JFK/EWR in either direction: to an airport on Sunday and Monday; from an airport on Thursday and Friday. Rate includes a free, first tank of gas, but free mileage is limited to 150 miles. Excess mileage is 10¢/mile. The Avis Kent Avenue location and the Budget Adams Street location (in the Marriott hotel) participate. The Marriott location is just a 5-minute walk from the Jay Street/Metro Tech subway station, which is served by multiple lines.
I am occasionally seeing the Avis/Budget deal work from the airports to some Manhattan locations, but am not seeing Manhattan to the airports for $9.99 with Avis/Budget.
No special rate code is required for any of these offers, but the Avis/Budget offer seems to be combinable with the AARP discount codes for AARP members, which would provide (minimal) primary third-party liability coverage, a free second driver, and a $5,000 cap on renter responsibility for loss of/damage to the rental car.
I recently took advantage of the Budget offer, from Brooklyn to both LGA and EWR. In each case, the rental cost, after tax, came to $12.08.

(Expect somewhat higher taxes/fees if you pick up at an airport, or in Jersey City.)