It's free if you walk.
how does it cost to get to Alaska, from New Jersey?
Most places ... The cost is money. From New Jersey to Alaska, they'll probably want US dollars.
Too many factors to give an answer on how much it will cost. It depends on where in Alaska you want to go and where you want to leave from in New Jersey. There is also how you want to travel, plane, train, or bus. If you choose train or bus you will need a passport to get through Canada. Try looking at travel sites like Kayak, or Expedia and put in the cities you are leaving from and where you want to go.