I really loved staying in the Oltrarno neighborhood - much more local and removed from the main tourist sites, yet only a short walk over the bridge away. Great restaurants and very close to Pitti Palace & Boboli gardens.
The apartment is perfect for 1-2 people, very clean and well-maintained. The wifi works very well. Giovanni is a great host - was very prompt in communication and quick to answer questions. Great restaurant recommendations as well for Il Santo Bevitore down the street.