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Seems like you are flying in from another country - so Newark and JFK will be your options for a non-stop, you won't be coming into LGA unless you connect within the US or Canada. I would go with whichever has the cheapest flights. JFK has the Airtrain to Jamaica station - from there I would recommend getting the Long Island Railroad to Penn Station instead of the subway, you won't need to leave the station and it's a very busy transit hub. A few bucks more but it will save 30-45 minutes and is more comfortable. Newark also has an Airtrain that will take you to NJ Transit rail that will also leave you at Penn Station, and avoids traffic. Should you end up at LaGuardia somehow, I would take a taxi but there are two buses the Q60 and Q70 that go express to subway stations that will get you downtown.
EDIT: Just seeing you are connecting in Seattle - but since those flights don't go to LaGuardia, my recommendations still apply.
The other issue is that there is a lot of heavy construction going on around LGA which could affect ground transport.
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