I wouldn't ride from JFK to Manhattan unless you're very confident of your route. Things aren't as wary as the 90s but there's still some grim bits of Queens and Brooklyn where you probably don't want to be lost and jetlagged on any bling bike (and by bling, any bike that isn't 90% rust). You can take your bike on the subway - get the Airtrain to Howard Beach and from their into central Manhattan. Not fast or pretty (NYC metro stations all look like public toilets) but does the job.
I'm not a destination person, I just amble. Ellis Island tops the Statue of Liberty, but take the free Staten Island ferry, there are some good views, and it's actually worth a pootle around Staten Island, over to Snug Harbor [park] for lunch etc. Very suburban and very different to the other boroughs. Cyclists still surprise 'em. You can circumnavigate it before returning to civilization.
Take the Roosevelt Island cable car for an interesting view (there's nothing much on Roosevelt Island though, unless you like concrete, and you can get that in Elephant and Castle).
Manhattan is prime ambling territory. Traffic is fine if you're used to London. Work your away around the outsides and nibble inwards on the cross streets. Central Park gets a bit busy, I recommend taking a ride over Brooklyn Bridge, through Brooklyn, stopping to catch the view from Brooklyn Heights back across the East River to downtown Manhattan - then pick up a route through Cobble Hill and the streets beside Atlantic Ave down to Prospect Park. Take a circuitous route back through Queens. It's worth investing in a good map or spending sometime with Google - provided you avoid the expressways, there's usually plenty of routes.
Probably because I've spent a lot of time in Manhattan, I like exploring the other boroughs. Will figure out a route to City Island eventually. My holiday policy is generally to get lost as often as possible.
