Any suggestions for Brunch? Or markets to see?
I arrive 8am and next flight is at 4pm.
It would take you an hour or so to get to the city, then you would most probably need to be back at the airport 3 hours before your flight. That leaves you from 9 or 9:30 am until 12 noon, not a lot of time.
If you are taking the bus or the Leonardo Express train, you'll arrive at Termini, the main train station. There's a very good food court (Mercato Centrale) there that focuses on quality local foods. I'd try to grab some breakfast there, and then start walking to see a few sights for the next few hours. On the way back to the airport, I'd grab lunch there, too (the Trapizzini are divine -- delicious bread pockets with savory stuffings).
would you recommend anything near the airport instead?