JFK layover

Is the 10 45 the time you need to be back at the airport or your flight time? I'm assuming that your second flight is an international one

Correct...International and 1045 is the flight departure. We would have to be back much earlier

Find someplace to store your bags. Then take the Airtrain to Jamaica station. From there I suggest taking the LIRR to Grand Central over the subway as it is much faster.

Grand Central is just a couple of blocks to Rockefeller Center. Go up to the Top of the Rock for a great skyline view of NYC.

Not sure how much walking you want to do as it will be cold in February. (Figure high 30;s) Times Square is just a few blocks from there. Or you could get on the subway and go just about anywhere.

Or if you want what I call the "Poor Mans" bus tour of NYC, get on the number M55 bus at 44th St between 5th and 6th Ave. It goes south down 5th Ave past the Empire State Building, the Flatiron building, Greenwich Village, City Hall, the Financial district and down to the Ferry Port. It then turns north and goes up 6th Ave past the site of the World Trade Center, West Village, Chelsea and then back to where you got on. It's a regular city bus. No commentary.

I might suggest getting off at the ferry terminal and taking the ferry to Staten Island and back. You get a great view of the lower Manhattan skyline and the Statue of Liberty. Plus, it's free. However, on the water in February is very cold.

BTW, 6th Ave is also known as Avenue of the Americas. For those of us born and bred New Yorkers of a certain age, it's 6th Ave.

You can pay for the Airtrain, Subway and buses with a contactless payment or Metrocard. For the LIRR, you will need to purchase a ticket. There are machines near the escalators to the platforms. (The Airtrain just started accepting contactless payments last month. You used to have to use a Metrocard.)

Give yourself at least an hour to get back to JFK from midtown Manhattan.

My only addition to Frank's great answer is that you can also pay for the Long Island Rail Road via their app, called TrainTime.

It's what I generally use as it allows me to skip the ticket machine (which in early February probably won't be an issue, but they can get busy during the holidays) and it will also automatically show you all ticket options that are valid for your trip. There are peak and off-peak tickets on the LIRR depending on what time and direction you are going -- if you select a trip in the app and go to buy a ticket, it will automatically show you all options that are valid.

Suggestions on where to store bag at the airport? Is there a service to hold them?

Perhaps your airline will have checked your bags on to your final destination. You definitely have time to make it into Manhattan for several hours on your layover!