The first option that ran through my mind was taking a Greyhound bus, and it costs $40. Any other options that you guys know of? The duration of the travel is not of essence. I'm ok if it takes longer.
Aside Greyhound (costing 30-60
USD), Rome2rio shows various other bus options including Yo Bus costing 20
USD. There is also a bus combination using BoltBus which supposedly costs 19-24
USD. MegaBus can get you there for as low as 11
USD one way depending on what day of the week you're traveling and how far in the future you book your ticket. The bus trip takes 4 to 4.5 hours
Another option is http://us.megabus.com/. It is cheaper and faster compared to greyhound. And it's less than $20.00 . It's way better than greyhound in my opinion.
According to Busbud a bus between Boston and New York City will run anywhere between 27 and 34$. A train ride from Boston to NYC will run anywhere between 74 and 255$.
Might be worth checking out "Carpool World", I've never personally used it but this seems like something you'd be interested in: https://www.carpoolworld.com/carpool_ride.html.
http://www.fungwahbus.com/default.html is rumored to restart service again soon. They go Chinatown to Chinatown. They were shut down in 2013 as an "imminent hazard to public safety" because of various safety violations.
At the time it was $10 per one way and it's a free adventure ride as well :-)
You can also try sRide (http://sride.co) . It's new free carpooling app.