I think we paid more than $80 for a hotel limo from central Manhattan to Newark. They told us it was the same price as for a taxi (flat rate).
My advice - if you want to see Manhattan, stay in a hotel in Manhattan! I know it can be expensive though.
I stayed at Grand Hyatt last time I was there. The hotel is almost like a part of Grand Cental station, with easy access to the metro. I guess it may be a little tricky to get there from Penn Station though, especially with a lot of luggage.
It took less than 10 minutes to walk to Times Square. Maybe a little more to Empire State building.
Ok, as I said, not exactly cheap - about $340 plus taxes per night.
Here is one of the rooms in Grand Hyatt.
Night view from Empire State building.
Daytime view from Rockefeller center (Top of the Rock).