JFK is the most convenient, however...
If the fare into LGA is significantly cheaper, then you've paid for a cab / car.

That said, a lot depends on where in Crown Heights your SO is.
If you are south of Eastern Parkway and not close to Franklin Ave. to the west, the best option is the 2 3 4 5 to New Lots, The B15 bus to the Airtrain (It's free at this stop)

If you are between Eastern Parkway and Atlantic Ave., you have a choice between the 2 3 4 5 and the Aor possibly C to the A on Fulton Street to the Airtrain. the A and C option will be faster.

As mentioned earlier, if you are near the Nostrand Ave LIRR stop, the LIRR to the AirTrain at Jamaica that will be the quickest and costliest. but it does not run as often as the others. The Nostrand Ave. stop is not well populated so I wouldn't recommend it in the wee hours. That said, Ms AMflier uses that station occasionally on weekday mornings and evenings without issue.

If you are close to Franklin Ave., then it's the S to the A to the Airtrain.