My first trip into the city on 'our' own (as new teachers... not knowing where we were going), we went to Un Posto and met up with a bunch of the other teachers from our school. Un Posto a lovely place with plenty of outdoor seating and greenery. It was an old farmhouse... and definitely has the feel of being out of the city, even though it's in the city. It was great.
We bought drinks at the bar and the restaurant set out a spread of dishes for us to pick through.