The two nearby airports are Philadelphia International Airport (about 35 minutes North from Newark DE) or Baltimore Washington International (BWI) Airport in Baltimore, MD (about 1 hour South of Newark, DE).
From these airports, there is shuttle transportation service that will bring you to Newark. Delaware Express is very reliable and has been to the University facilities numerous times.
DELAWARE EXPRESS SHUTTLE & TOUR +1-(800)-648-5466
From the Philadelphia Airport (PHL): Dial 24 from Ground Transportation phone in baggage claim. ARRIVALS AT TERMINAL F: Get bags, go to term E, dial 24.
From the Baltimore Washington International Airport (BWI): Dial 800-648-5466 from baggage claim payphones. A Delaware Express driver will meet you in 2nd lane over from baggage claim.
There is Amtrak from Baltimore, Philadelphia, New Jersey and New York, depending on where your flight lands, to Wilmington and Newark, DE. You may then use JFK International Airport in New York or Newark Liberty International Airport in New Jersey, as your alternatives.
AMTRAK rail services +1-(800)-USA-RAIL