We spent 6 nights in Gubbio last November and we loved the town.
I don't know what day of the week you're going, but Tuesday is market day, 3rd Sunday is antique market, 4th Sunday is organic food. A medieval festival is scheduled for September 21–25, 2022. That could be a reason to visit then or not visit then.
Gubbio has the 2nd largest theatre in the Roman empire (the 1st is in Rome) --- if you only have one day, though, this can be skipped.
Some of the picturesque streets are Via Baldassini, Via Galeotti, Via Piccardi, XX Settembre, Via dei Consoli, & along the river leading to Piazza 40 Martiri. On Via dei Consoli look for the "doors of death," skinny doors next to the main doors which were probably actually NOT for carrying coffins out.
Fontana dei Pazzi --- see: https://www.atlasobscura.com/places/fontana-dei-matti
The Museo Civico e Pinacoteca in the Palazzo dei Consoli has views from its loggia & medieval rooms, and the kind of paintings I like (e.g. apostles sitting in a semi-circle so that all their identical bare feet look like they're at a foot conference, and another in which a baby Jesus looks bored out of his wits.)
Sant'Agostino has frescoes (like a nice lurid Last Judgement) & other paintings, but it is not always open, so a weekend might be best. More frescoes in the Chiesa di San Francesco & cloister.
The iridium gorge (Gola del Bottaccione) is a 20 minute walk from Piazza dei Quaranta Martiri. It's where scientists could see the iridium layer they predicted, an important indication of a comet strike being the cause of the extinction of dinosaurs and other creatures. Just mentioning it in case you like that sort of thing. My husband, former geologist, enjoyed it as a sort of pilgrimage, and I thought it was cool.
Our two favorite restaurants are side by side: Orto Osteria dalla Terra and La Cresciamia. I'm pretty sure we needed reservations for lunch, even in November.
Taking the birdcage lift to the top of the hill is really fun, especially on a foggy day. If you are nervous about hopping into it while it's moving, the guy who helps you get in can hold it still for a little bit.
I do not think you need a guide, but I am not a tour-compatible person, so I am biased --- it always seems like a guide is going too fast or too slow, speeding me past things I want to see and then spending "endless hours" telling me about things I don't care about while I stand there. I can see, though, how if you only have one day, a guide could help you see more things efficiently without getting lost and could answer your questions.
