From the airport of Florence Amerigo Vespucci you may take a taxi to downtown (20 minutes) or a bus shuttle to Santa Maria Novella railway station.
Palazzo Strozzi is just 5 minute walk from the ralway station of Florence Santa Maria Novella.
You may obviously find hundreds of hotels in the city centre of Florence. The following list is only a very small subset.
Hotel Adriatico ****
Hotel Augustus ****
Hotel Cavour ***
Hotel La Residenza ***
Hotel Pitti Palace ***
Hotel Duomo ***