Iberia has low fares from New York JFK to Madrid, Spain down to $381 round trip in February and March, $405 in April-May, late-August-late Oct, then back down to $381 through November. Spring and fall months combine fewer crowds with lower temperatures. But if you want caliente Madrid in peak summer, Iberia round trip fares are only $505 to $520 to Madrid and several other places in Spain. Portugal is discounted too.
Iberia Airlines New York JFK – Madrid, Spain MAD nonstop
Iberia Airlines New York JFK – Madrid, Spain MAD – Tenerife, Canary Islands, Spain TFN – MAD – JFK