Iberia and American Airlines have many dates selling for $247 and up for direct flights NYC-MAD.
The flights go all through the winter and well into spring. Latest flight departures are mid May.
Please note these are Basic Economy flights that don't include a checked bag. They do however include a carry-on. Regular economy is about $100 more per ticket.
You can check Google Flights to find dates that work for you and then book with American Airlines/Iberia/Expedia/Priceline etc'.
If purchasing the flights with UR points, you'd be paying as little as 16,500 points for a round trip ticket to Madrid and you'd still earn miles for the flight!
Here is how to get it even cheaper with hidden city:
Search for a round trip JFK-MAD and find cheap dates that work for you.
After you've got your dates, switch to multi city search.
Plug in the outbound and return as before.
In the third segment make the flight date the day after your return flight from MAD-JFK. Search for flights from NYC (make sure LGA and EWR are included) to BOS, PHL, MIA, YUL, YYZ.
You should be able to take another $15-50 off the total cost.
Cheapest I have seen so far was $211 for a round trip direct flight JFK-MAD!
Post what deals you find.
Sample dates:Nov 9-18
Nov 11-18
Nov 13-21
Jan 12-20
Jan 16-26
Jan 19-26
Jan 19-27
Jan 23-Feb 2
Jan 28-Feb 9
Feb 20-27
Feb 20-Mar 2
Feb 27- Mar 9
Mar 26- Apr 8
Apr 20- 28
May 6-13
May 12-21
May 13-21
@Dan