Most of the main sights in Florence are within walking distance of each other, but it's a good idea to purchase a Florence Card, which includes access to most of the museums and public transportation. For day trips, take the train or bus from the Florence Santa Maria Novella train station. Train tickets can be purchased at the station, but it's a good idea to book online in advance to save time and guarantee a seat.
If you have more time, consider taking a wine tour in the Chianti region or visiting the medieval town of San Gimignano. If you have less time, prioritize the top sights and skip the day trip to Cinque Terre. Make sure to book your restaurants in advance, especially for dinner, as they can get crowded quickly.