Literally a few hours in Rome

I am currently in Albania for business, and my company’s corporate travel service totally screwed me with the most ridiculous return flight route ever.
Tirana, Albania> Rome, arrive at 7:45pm. Then layover until my next flight leaves AT 6AM. To.....AMSTERDAM.
4 hour layover in Amsterdam, then 9 hour haul to Washington, D.C..
Anyways, end of rant. My hours in Rome are too weird to get a hotel for the night. But I figured I might as well go into the city and get a nice dinner, just walk around for an hour or two, then catch a cab back to the airport.
First- is anything about this plan bad? Like will I have a problem finding a taxi back to the airport or leaving and reentering it? I understand the airport is 30-40 minutes from the city?
Second, I have never been to Rome or Italy. Where should I get a cab to for the purposes of just getting some dinner and walking around? Any particular recommendations on what to eat this time of the year?
Thank you.