From the hotel what is the means of transport (bus, shuttle, metro) to get to New York and at what price? And for the return is there an hour to still have transport?

There is a bus stop across the street. Take the 320 bus that will take you to NYC port authority. I think it was $2.75 each way per adult. Make sure to get a bus info flyer from the front desk. It was very helpful for us to know at what time the bus was expected so we could plan better.

NJ Transit Bus 320

Bus

Bus line 320 with a close stop just in front of the outback steakhouse restaurant (which by the way and to try), for the price it is $ 7.50 per person and trip, no advantageous rates for several trips unfortunately, the ticket is 'buy directly at the stop, at a terminal, if you have to make the round trip, I advise you to take it directly, more practical, the bus will drop you off at bus authority (bus station near times square).