Enjoying Florence on a tight budget

Walk (or take the bus) across the Arno up to Piazzale Michelangelo, which has breathtaking views down on Florence. Perfect at sunset.

Biblioteca delle Oblate... library that is a block or two from the Duomo and has very nice views of the Duomo, particularly from its cafeteria, which has filling, tasty, cheap food.

Above Piazzale Michelangelo is San Minianto Church, which has a service with Gregorian chant on Saturdays, if I recall correctly. The church also has a graveyard that includes people like Carlo Collodi, the author of Pinocchio.

The markets are free and always interesting. Here's a link to a list of the best.

Also, if the weather is nice get up early one day and just go out and walk around. Cities are always more interesting early in the morning before the hordes descend.

Visit Santa Maria Novella nr Train station. It is a centuries old pharmacy that now sells exquisite parfums, soaps etc. no charge to look and admire the the ambiance and beauty of a ancient pharmacy.
A cheap bus ride can take u to Siena for the day.
Also a cheap busmride can take u to nrby Fiesole tomenjoy views and sunset.

JS beat me to it. The bus to Fiesole is a regular Florence city bus and so is cheap. If you have a clear day, the views are great (I was there in March, so I can't speak to what it would be like in November).

I'll second the walk up to Piazzale Michelangelo and further up to very old San Miniato and the cemetery (Cimitero delle Porte Sante). Visiting info/hours here:
https://www.visitflorence.com/florence-churches/san-miniato.html

The monks also have a pharmacy that sells handcrafted beeswax candles, herbal products, jams and other goodies. "Open every day generally from 10.00 to 18.00, with a break from 12.15 to 16.00."

https://www.sanminiatoalmonte.it
Some more background info in English: http://www.museumsinflorence.com/musei/san_miniato.html

For a small but impressive collection of sculpture, Loggia dei Lanzi on Piazza della Signoria.
https://www.visittuscany.com/en/ideas/loggia-dei-lanzi-an-open-air-museum-in-florence/

Piazza della SS Annunziata:
https://www.visitflorence.com/florence-monuments/piazza-ss-annunziata.html

You'll probably recognize the famous della Robbia bambini on the facade of Ospedale degli Innocenti, on one side of the piazza. This Brunelleschi-designed structure was one of the first foundling hospitals in the world. From the center of the piazza, look down the street for a unique view of his most famous accomplishment: the dome of Santa Maria del Fiore. On the porch of the building, look for the grated window that once contained a rotating wheel on which an infant could be safely and anonymously abandoned out of the elements. A little background:
http://www.arttrav.com/florence/ospedale-degli-innocenti/

And Basilica Santissima Annunziata on another side of the piazza:
https://www.visitflorence.com/florence-churches/santissima-annunziata.html

The frescoes in the entry cloister alone puts it on an art-lover's must-see list.

Santa Trinita: the Sassetti Chapel in this church is fascinating as the artist painted the contemporary figures in the cycle - including himself - as they really looked! You'll also catch glimpses of 15th century Florence in some of the backgrounds.

https://www.visitflorence.com/florence-churches/santa-trinita.html
http://romananglican.blogspot.com/2015/05/the-sassetti-chapel-in-santa-trinita.html

A couple more churches:
Santo Spirito in Oltrarno:
https://www.visitflorence.com/florence-churches/basilica-santo-spirito.html
Monday - Saturday (Wednesday closed) from 10.00am to 1.00pm and from 3.00pm to 6.00pm; Sundays and religious holidays from 11.30 to 13.30 and from 15.00 to 18.00.

Orsanmichele:
https://www.visitflorence.com/florence-churches/orsanmichele.html

San Marco:
https://www.visitflorence.com/florence-churches/san-marco.html
The attached monastery museum is WELL worth the small entry fee: a fave of mine. It has some goofy hours/closure days though:
https://www.visitflorence.com/florence-museums/san-marco.html

And, of course, Santa Maria del Fiore (but not the dome) is always free:
https://www.visitflorence.com/florence-churches/duomo.html

The British Institute library is free --- I sat there on a sofa in the lounge area for hours one day and looked at all the books about the 1966 flood. One photo showed the building itself on its flooded street and another showed the street where our airbnb apartment was, all under water. Other photos showed many of the famous places you'll see in Florence, both inside and out, in deep, filthy water. Be sure to look for all the markers all over town showing the water levels.

Also look for the Clet Abraham street signs and the other street art.

Thank you all for the wonderful suggestions! We are in Florence making good use of them -- we've got one last full day tomorrow and already sad to be saying goodbye. I loved the Biblioteca Oblate especially. Beautiful view, laidback vibe, and great espresso. Grazie!!

This is a great post and I will use this information as I plan our trip for August 2019. Thank you OP for the question and responders for your thoughtful comments.

Sounds like you enjoyed the Biblioteca as much as I did! Glad you found the recommendation worthwhile...