Basically anywhere in Europe (not just AMS) should be possible with such an award like Italy or Spain depending on what tickles your fancy as it should be the same number of miles required with Kris Flyer. Connection would always be in FRA if you take the SQ flight JFK-FRA-JFK or FRA / MUC if you go LH all the way in which case you could also go from / to EWR. Your onward flights from FRA / MUC to anywhere in Europe would be in LH C (no F on those short hops and C is only a Y seat with the middle seat empty but okay for 1-2 hrs flight.

The First Class Terminal in FRA is truly excellent so if you decide to go one TATL (trans-atlantic) sector in F on LH then you can use it. You would not stay in FRA for your holiday but only connect there. Not bad if you like to spent time in Europe.