Plenty to do in Florence on a Monday. Actually, if I only had a couple of days there, I probably would not do the museums anyway, I'd save that for a longer stay.
Pretty sure the churches are open, and if so, the Duomo should be on your list. It's pretty much the symbol of Florence. If the dome is open to walk up to the top, it's a cool view from the top. About half way up you get to see the fresco on the inside of the dome, up close. The fresco is of Dante's inferno and this one doesn't leave out anything. Hot poker up a dudes ass. Yep, a few of those. Naked people being eaten alive by demons. Plenty of that. Thanks Dante!
Even if the Duomo is closed, just seeing it from the outside is an experience. It was refurbished in the 19th century, I think and it looks close to what it looked like in the middle ages. Brightly colored marble, painted statues. It really is spectacular.
The Ponte Vecchio is another cool stop. It's a bridge with shops and homes built on top of it, allowing only a narrow passage. It was built in the 13th or 14th century so it is an actual medieval bridge, pretty much continuously used by merchants for 700 or so years.
The Piazza della Signoria, just up from the Ponte Vecchio is an awesome public area, filled with statues which are reproductions of famous statues housed in museums in Florence, including a David replica (but not the level of detail as the actual David).
Another church that might be open since it's not really a museum, is the Basilica de San Lorenzo. It's burial place of several members of the Medici family. Very cool marble mausoleum. Serious wealth those Medici's. Those dudes knew how to die in style.
I'd also recommend checking out Mercato Centrale, an inside open air market just north of the Basilica de San Lorenzo. Lots of vendors with booths, kind of like the West Side market in Cleveland, if you've been there. We picked up the best piece of pepperoni I've ever had there. Still have fantasies about that pepperoni. For a good cheap lunch, visit Da Narbonne in the Mercato. If you're adventurous, try a tripe sandwich. I thought it was OK. The flavor was great, but tripe is mushy my nature and they lay it on thick. Pulled off a couple of layers and it was much better. Also had a great roast beef sandwich there and a good bowl of a local soup/stew called Ribolita.