You need a 2nd. Cruise ships book double occupancy so if you are by yourself if will be double the listed price for the single occupancy. Much cheaper to find a friend to go with you.
You really can't get anywhere from NYC in 4 days. Plus the water in the Atlantic is so choppy up there.
Carnival has one 4 day one. It's only port of call is Saint John, NB. They also have a 5 day that goes to Halifax and Saint John.
The per person price respectively starts at $250 and $340.
Royal offers a 5 night Bermuda cruise starting at $450 per person.
You might also want to look at NCL. Those 3 are the cheapest cruise lines.
Seriously though for a first cruise I'd never want to do those itineraries. Choppy water, older ships, worse port of calls. My biggest tip is to fly down to Florida or take the train or something. Go out of Florida where you have better prices, better ships, better ports of call, and a better vacation.