Thank you to everyone who posted their ideas! I'll be arriving at LGA on AA, departing from JFK on AA international. Final destination is Riga.
I thought about going into Manhattan, but (if I accept the suggested times for NY Airport Service shuttle) I would have only 45 minutes between drop-off and pickup in Midtown!
I considered renting a car for a few hours to just drive around, but the price was north of $100 so it didn't seem worthwhile.
So, it looks as if I'm going to take a shuttle from LGA to JFK and then just poke around and surf the web.
I did notice that the FAQ for
New York Airport Service appears to have been hacked...notice the answer to the first question