Terminal 8

You have 3 hours transfer time - enough for JFK. You should be concerned if Swiss gets delayed more than 1 hour(it will give you less than 2 hours transfer time).
JFK_E

Hi Tommy,
You can eat at Terminal 4, 3rd floor, food court - there are restaurants there. Smoking is permitted outside the terminal.
JFK_E

Visitors are not allowed to go to the gates. They can meet you by the baggage claim, on the first floor at Terminal 8.
JFK_E

Mexicana is at T8, Aeromexico is at T1.
JFK_E

Go to the third floor of the Airtrain station and take ANY train. Listen to the announcements in the train - get off when they announce Terminal 8.
JFK_E

You will be arriving at T8, they - at T1. You can meet at either terminal, 1st floor, by Ground Transportation counter.
I will assume the hotel is located near Times Square - West 42nd street - here are some of most common options that you have in this case:
1. Taxi(the fast and easy one)
Yellow cab (from JFK to any point to Manhattan) costs flat rate of $45 + bridge toll($5.50). The price is for the whole taxi, not per passenger.
2. Public(the cheap one)
Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one). Then take subway line E to 42nd street stop. Cost-$7.25/passenger.
3. Shuttle
There is shuttle(look for it at Ground transportation
counter or Welcome Center) that goes to any hotel in Manhattan for $18.50 per person.
4. Express Bus
NYAS(New York Airport Service) bus will take you express to Times Square for $15/passenger. The bus leaves every 20 min in front of each JFK terminal. You can buy tickets on the bus or from their representative in front of the terminal.
JFK_E