Sounds like you'll have a nice trip.
It is a a bit of a hike, relatively, from Newark to NYC but easily doable. There is the PATH trains, NJ Transit trains & buses and some shuttles too. For getting from LGA to Newark you can drop your bags at certain hotels and storage centers in Manhattan for a few hours in the city as to not waste a day just getting from the airport to the hotel. There should be a list of those services somewhere here on FT. They're pretty cheap and let you do some exploring.