I use avistar (www.avistarparking.com) when I infreently fly out of Newark. Close to the airport, cheaper than on-airport prices, and frequent shuttle buses.

Depending on when your flight leaves you may wish to consider spending the night at a hotel near the airport; many of them offer up to two weeks free parking. When I do that it's usually a wash costwise and I don't have the stress of getting to the airport early.

If you decide to go with the hotel option, check out the Wyndham Garden Hotel. Recently refurbished, friendly staff, protected parking, frequent shuttle and low rates with up to 2 weeks parking included make this a great way to go. You need to call the hotel to get the special rate with long term parking included.

Are you aware of www.parksleepfly.com

I have used them several times. The hotel tells you what section of their parking lot to use.
You also have the option of staying at the hotel if you get back late and don't feel like driving home.

Airport Parking offers a paved, lighted and fenced facility with 24-hour security. Just minutes from the airport, with safe and secure parking and free shuttles 24 hours a day, Avistar-McClellan Parking is a great option when traveling from Newark Airport.

I use www.OneStopParking.com they are great! Montreal they have 2 locations you park at the Sheraton or Holiday Inn right near the airport. I save a lot of money using this company. Check them out.