OT Newark to Manhattan

Hi there -- I am planning a trip to the East Coast in November. We're going to a concert in Manhattan (though I'm going to have to find out WHAT part of Manhattan because there appears to be different parts!) and will probably stay out there 4 days or so. Hotel prices are very expensive so I'm thinking we can just stay in Newark because I heard it's easy to get from there to NY.

I'm looking at the ground transportation options and it looks very confusing. Then again, it always does to me :D Is it highly complex? We'll be flying in and out of EWR and we'd probably spend two days in NY and one in New Jersey. I'm looking at trip planner options at the transportation websites and because it appears that there are connections across state lines, I'm not finding anything that will tell me everything I need to know.

We usually go to Boston a couple of times a year (love MA!) and it feels more like home. This is a new and challenging experience.

One last thing is we wouldn't be adverse to staying in NY but since I don't know it, I don't want to stay somewhere inconvenient (as if Newark isn't?), in the multi-hundreds per night, or scary.

Thank you for any and all information! This is in the planning stages but I'd like to start working on hotel reservations. If there's anything I must see, I'd love to hear about that too. I only know what typical tourists know...