Our first day in Florence began with a trip to Piazza del Duomo, a square in the heart of Florence that houses the medieval Cathedral of Santa Maria del Fiore (once the largest church in Europe), Brunelleschi's Dome, Giotto's Bell Tower, a baptistry, and a museum. Admission to the cathedral is free, but you'll need a €15 ticket to explore the other sites on the piazza. This will also give you the opportunity to choose a time to climb the dome and bell tower so you aren't stuck waiting in yet another long line.
At 463 steps, it's a long climb to the top of the dome, but your hard work will be rewarded with views of Florence and the surrounding hills of the Tuscany region. The bell tower has almost as many steps and similar views, and the baptistry allows you to rest your legs and admire the mosaics until you are ready for more walking. The museum is a wealth of medieval, Renaissance, and Baroque masterpieces that took up a surprising part of the afternoon to explore.
Be sure to check opening and closing times for each building before you go — we thought we knew the schedule, but there was a different one posted on the doors of the baptistry when we arrived, so we had to rearrange our plans a bit in order to see everything.