A taxi from JFK to Manhattan has a flat fee of $52.80, plus a $4.50 rush hour surcharge (4pm-8pm weekdays), plus a $2.50 fee for trips to Manhattan south of 96th street, plus any tolls and tips. So you're likely looking at somewhere between $60 and $70. Here is the official information. If you are uncomfortable on the subway or have lots of luggage, I would recommend this.
However, this is also very easily doable on the subway (total cost $7.75 per person), which is what I would personally do assuming I had a manageable amount of luggage. You would:
- Take the AirTrain to Jamaica station. There is a $5 per-person fare on the AirTrain which you pay when you leave the AirTrain at Jamaica station.
- Take a Manhattan-bound E train to the 7 Av station in Manhattan, located at 7 Av and 53rd St. Your hotel is one block away at 6 Av and 54th St. Subway fare per person is $2.75.
My advice would be: when you land, check the official MTA website. It will indicate if there are delays or service changes on the subway lines. If there is some kind of unexpected service change on the E that you don't understand, then you're forewarned and can take a taxi instead. Otherwise, however, by NYC standards I would consider this to be a very simple subway trip.
(Finally, a friendly tip -- in real life the 'Avenue of the Americas' moniker is basically unused; New Yorkers just call it 6th Avenue.)