If you have luggage and/or a time constraint then a cab or uber/Lyft would be easiest. It can cost as much as 60 bucks tho. If there is NO traffic (very rare) it would be about a 25 mins but expect closer to an hour. Public transport would take you at least 2 hrs.
For me i found taxi is the cheapest if you have 2-3 people, i paid $40 only to taxi with all luggage and us! Closets to exit too!
I'd take public transportation. First floor at LGA catch the Q70 bus to Roosevelt. Then E train towards Jamaica. Switch trains at archer station to the JFK air train. Might cost you ten bucks, but will take an hour or so.
The quickest path seems to be getting a cab, but you can also take public transportation but it will take over an hour and you have to transfer to get there
You can either take an Uber or if you're driving you would take the Grand Central towards the lie and take the Van wyck expressway to JFK directly.
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