It doesn't look like AA fly direct from DTW to EWR or JFK although they do have flights to ORD where you could connect to BA.
Anyway if you have to come back via NYC then I would only look at LGA then JFK as suggested - it will take around 20 mins in a cab to get there maybe a little less. To get to EWR you need to go all the way in and out of Manhattan then into New Jersey where i'm sure the taxi driver will charge a significantly higher price (it wont be metered)
Chessy