Originally Posted by AirD0c
You can redeem BA Avios on Iberia to avoid fees. Haven't done it myself and doesn't seem very straightforward but apparently possible. See this TPG post:
Otherwise I would probably use United points. You have enough for economy or you could transfer an additional 30k UR for biz. I think UA flies direct to Madrid from EWR. Or you could fly LH via Frankfurt or Munich; Tap via lisbon etc.
Using Avios on Iberia instead of British Airways lowers the fees and also opens up a lot more redemption options, as seats are available to Iberia Plus members that aren't available to oneworld partners.
You can of course transfer your Membership Rewards points directly to Iberia, but you will miss out on any transfer bonus that you'll get by first transferring them to BA (though none are currently available to my knowledge).
Keep in mind that in order to convert BA Avios to Iberia Avios, your IberiaPlus account has to be open for 3 months AND have some activity (transferring in 1k MR points will work). Not a bad idea to open an Iberia acct just to get the clock going.
That said, I like AirD0c's idea of focusing on United. If you're flexible with dates you could get onto a direct to Madrid, and return home from Barcelona on partner airlines (connect them with a cheap Vueling flight). Booking this as a round trip will allow you to count NYC as a stopover on one side of the trip, thus adding a "free one-way" to really extract value from your miles.
NYC - MAD (United or partners)
BCN - NYC (United or partners)
NYC - XXX (United)
This is a double open-jaw with a stopover for only 60k miles in Economy! You could of course take the stopover at the beginning of the trip instead.