+1 with both slawecki & SFO777

your travel/stay ratio is out of balance and if you factor running around Tuscany, it gets worse. I'd second slawecki's advice of just doing FLR if you want to go to that area and SFO777's point to skip the train and fly to destination (at least inbound as it looks like you are connecting in (BA?) to LIN). Outbound, if it's MXP, do yourself a favor and stay at the Sheraton - very easy access to the terminal and the flights to NY (I'm guessing AA 199 but DL has one at roughly the same time) is a 10AM departure.

If you do go to Florence, I can recommend the Hotel Lungarno. It's a nice, intimate hotel, centrally located and owned by Ferragamo overlooking the Arno and the Ponte Vecchio. I've linked a picture from the balcony of our room last time we stayed there. If you do stay there, make sure to book a room overlooking the river as they have other rooms that don't. On the romantic scale, my wife says you can't beat sitting in the lobby bar, sipping some prosecco, surrounded by Cocteau and Picasso drawings while overlooking the Arno...

To eat like locals, just go across the street to Mamma Gina's (I know, cheesy name). It's a simple trattoria with excellent food (ribollita, tagliata con rucola, pastas...).