John, here are a few ideas to get you started:
San Miniato al Monte and Porte Sante cemetery (free): just above Piazzale Michelangelo. She’s a a very old and interesting church, and the cemetery is just as interesting for a wander. Great view of Florence from both church and piazza. Take a virtual tour of the church here:
Loggia dei Lanzi and Piazza Signoria (free):
Piazza Santissima Annunziata is a favorite of mine. It’s just around the corner from San Marco (unfortunately closed on your Sunday) and you can see Andrea Della Robbia’s sweet, famous tondos on Brunelleschi’s Ospedale degli Innocenti; one of the very first foundling homes in the world. Look for the grated window on the front of the building that babies could be passed through, and which replaced a rotating wheel for the same purpose.
Santissima Annunziata church (on same piazza; free) is also well worth stopping into, and you’ll get an interesting perspective of Brunelleschi’s dome on the Duomo from the piazza.
Boboli Gardens at Palazzo Pitti: as they’re part of the Pitti Palace complex - which is a state museum - entrance will be free. They cover a lot of ground so no worries about being overrun. All of the galleries at the palace will also be open so take a peek at any which aren’t too busy. Use this site for info only as you will not need tickets, and the ‘official’ website for the Pitti is in disarray right now. Scroll to the bottom of the page and click the text for "English."
Santa Croce (Sunday afternoons;fee):
Santa Maria Novella (fSunday afternoons; fee):