We will be staying only one night in Florence. We are coming from 4 nights in Tuscany, need to return rental car. We are going to Venice afterwards by train.
What is the best area to stay in to get as much of the full Florence experience as possible? I know the near the train station would be convenient but I don't want that to limit us since we can take a cab and have no time restrictions.
Hotel choice is about having the best location for a 24 hour period.
Near the Duomo, or Ponte Vecchio would put you right in the middle of things. We stayed near SMN station and it was only a 10 min walk to the Duomo, as Florence is quite compact.
Look at a map of Florence. The area between Piazza San Lorenzo and Ponte Vecchio/Uffizi, passing through Duomo and Piazza della Repubblica, is the busiest. Basically Disneyland in summer.
If you want slightly quieter, and more like Florence as it used to be, look at the Oltrarno (beyond the Arno=south bank of the river). However on that side, Via de guicciardini (between Ponte Vecchio and Palazzo Pitti) or on Piazza Santo Spirito, it’s pretty busy too.
I'd vote Santo Spirito area! It charming and a bit less touristy but is still very close to all the touristy spots.
We have rented an apartment in the Oltrarno on Piazza Passera which is not far from the Pitti Palace and loved it. Also rented an apt. not far from Piazza Santa Croce just down from the Bargello on Via Vigna Vecchia and we enjoyed this location too. These stays were for 5/6 nights. For one night I personally would stay closer to the train station. For 2 and 3 night stays we have stayed at several places just a few minutes walk from the train station on Via Faenza, just a few steps from the Medici Chapel and a quick walk to the Duomo.
If you only going to stay for one night, just about anywhere in the historic center of the city would be fine. Your dance card will be full enough just visiting the standard list of sites so you aren't likely to have time to even begin to experience a particular neighborhood. If you are staying for a longer period, then selecting a locale to call your own becomes more important. With a couple of days at your disposal you can relax a bit and take your time exploring both the 'famous' sights and the interesting aspects of the common streets, shops and eateries around you.
For just one night, I would stay between the Duomo and the train station. As others have said, Florence is very compact, so if you are in that area, it will be easiest to get to/from when arriving and departing and also you will be close to many things to walk to.
