The farthest I traveled was the city of Rome, where I spent two days exploring the Colosseum, Pantheon, Trevi Fountain, city streets and restaurants! We had a terrific hostel experience and while we came back very tired, we couldn't have asked for better weather (it was mostly sunny in Rome), or better opportunities!
Rome is the farthest I've traveled! Outside of Rome, my friends and I took the train to I Gigli, a major mall only a few stops from Florence. We did some major shopping, as it is a bit inconvenient to get there, so we figured we would make the most of the commute.
I was at the Santa Maria Novella train station multiple days this week, as that was my main form of transport. Aside from a few Ubers we took in Rome, every other commute has been by foot!
The most interesting place was probably the Vittoriano Monument in Rome. While it was not an immediate recommendation I received from others, we found it to be the grandest and most beautiful building we visited. Entry was free, and we walked up a beautiful staircase into the most gorgeous piece of architecture, with an internal museum and a restaurant terrace overlooking Rome.