For EWR, since parking is outrageous (Of course it's the NYC area) check around for a package deal with some discount for a week or longer parking.

I received this card from AMEX for some discounted parking at one of the big company lots near EWR. I threw it out (now I wish I didn't, I could have help you Mr. Nice) but if I remember there were deep discounts for weekly parking and I think you also earn M-P miles.

Check with AMEX. I don't remember the parking company name.

Sorry I can't be of more help but it's this age thing.