You won’t have any trouble getting a ticket for a Baseball game so long as the Yankee’s are at home, they generally play about 5 consecutive games. If the Yankee’s aren’t at home you could do the Met’s but they’re based in Queens.
Most tourist attractions are obviously in Manhattan and a great way to see New York’s 5 boroughs is do a couple of days on the hop on hop off bus, we have generally boarded near Times Square which is a great place itself to visit and take in a show if that’s your thing. Don’t go on a Monday though as a lot of theatres are “dark”, closed that day.
The subway is great for covering long distances but if all your party is able walking is brilliant as every corner you turn there’s a landmark that you’ve seen on TV.
China Town and Little Italy are great for food and a trip to the Peace Tower, the site of the Twin Towers is a must, pay to go in the museum, it’s worth it.
The boat trips on the Hudson are good usually accompanied by a comedic guide, I’d just take a boat that passes the Statue of Liberty rather than the dedicated one that lands there as you see more of Manhattan and they usually sail right past the Statue so you get a great view.
Piers 45 and 57 are brilliant attractions, Sunday is a great day to visit 57. Central Station is well worth a visit, it’s absolutely stunning.
As I said earlier I really enjoyed the Intrepid maritime museum that features the aircraft carrier and Growler Nuclear Submarine
There’s really so much to do, I’ve not seen it all despite 4 visits!
Plan your time there, it can be expensive but we generally have a decent breakfast and then a light evening meal and treat ourselves to a nosebag in a good restaurant at least once, it will be about £100pp now I think. However there’s many cheaper restaurants, my favourite is John’s Pizza but as you’re staying in Newark is should be less expensive.
Also don’t forget Rudy’s Dive Bar on 9th Avenue, $3 for a pint and a free hot dog.
I’ve looked up, Newark to Manhattan is best by train, just over 30 minutes.
Buy a decent guide book before you go and take advantage of the “multi site” tickets where you can budget before you go, really good discounts on attractions.
You’ll have a fantastic time.
Edit, forgot about the Empire State Building, best at night for a spectacular view of the City. And as
@Threeinarow said visit Central Park, it’s huge and loads going on there.