Try these for starters...all under newark/elizabeth, off exit 13A of the NJ Turnpike:
Courtyard and Residence Inn by Marriott
Country inn & suites.
the Country Inn has a package but you need to call the hotel direct and ask about it, as i don't think the price on line includes everything (ir, parking and room but not shuttle, or room and shuttle, parking extra)
I have left my car at the Courtyard and RI on several occasions.
These hotels are opposite an outlet mall and adjacent to a Ruby Tuesday restaurant.
Click the link in my signature for ny blog about cape liberty.
Most of the hotels will NOT have shuttles but you can get a cab/car service to the pier for about $45 plus tip. (usually when the hotel calls for a cab, they get you a car service.)
I have used www.blackexecutivecars.com
in the past and have been very happy so that may be an option as well.
Hope that helps! We just got back last sunday from a 21 night B2B on explorer...wish we were still there!