What Tim said is true about Long Island right now...not much to see or do other than some restaurants and in the short amount of time you have, not really feasible. I can suggest one thing: Stay in the Garden City Hotel overnight. It is nearby (about same distance to Manhattan in the other direction) and if you're averse to taking a cab, you can take the Airtrain to Long Island RR Jamaica train station & take the Hempstead branch to the Garden City train station which is literally 500 ft or so from the Hotel. I suggest this only because all the hotels near JFK are absolute crap and are in a sketchy area. You will not want to wander about outside the local hotels, I assure you.
There is shopping 1 block away from the GC Hotel on Franklin Ave with many nice restaurants. If you want high-end, the Polo Steakhouse within the GC Hotel has you covered. There is the Red Door Spa in the Hotel to relax and pamper your wife. There are nearby golf courses/countryclubs but of course, this is winter & your time is limited. There is a chocolate expo going on now nearby at the Cradle of Aviation Museum. The GC Hotel concierge will have many other suggestions, I'm sure.
Garden City Hotel:
Garden City Hotel in Long Island, NY | The Garden City Hotel