flight problem?

So I was finally able to retrive my flight information from the delta website and as I was expecting my itinerary was changed. However, obviously they didn't get it right. I arrive to JFK at 3:15 pm july 5th, and my flight to Mexico city? at 9:15 am of July 5th!

I had to read it three times, at first I thought they had put me in a flight the next morning, which would have been annoying but at least possible, but no, they totally made a mistake on the schedule!

This however is giving me the chance to try to score an extended layover in NYC for a few days without having to pay for a ticket chance. So now what should I do? fly a few days earlier from Milan, or a few days later from NY...

I also need someone to take my room here!