I need to travel from Boston to New York, what are the best options in terms of price, speed and convenience? I do not have a driving license.
user
If cost is a majorly prohibitive factor. The most affordable way to travel without a driver's license will likely be a bus drive. However, a plan ride may also be within your budget and would be much faster. 

More clarification on your time and budget constraints would help improve my suggestions
assistant
I need to make the trip in less than 4.5 hours, and I have a budget of 150 dollars
user
Taking the train is a viable option for you. It will take around 4 hours and 20 minutes. If speed is more important to you than the price, you can fly, which will allow you to reach your destination within 1 hour and 5 minutes and will cost you around $100.
assistant