Bologna

Staying for a week? When we’ve done that, we got an apartment, which gave us an affordable kitchen for fixing breakfast and any other meals we wanted to make, plus a fridge and clothes washer, besides just a bed and bathroom. The owners are often helpful with ideas for restaurants, sights, and getting around. Look at www.Vrbo.com . The area right around the train/bus station is kind of rough, so look farther south.

In October 2022, we stayed here https://t.vrbo.io/TBOz0HMPuBb . It’s at the top of the building, up several stairs, with some parts of the ceiling sloping low, but was nice, and a lovely deck off the kitchen.

Late September 2021, we stayed here https://t.vrbo.io/ucrNVsEPuBb . Newer, larger apartment and very nice furnishings, and a great location just outside the ring road, just a 12 minute walk into the central city Piazza Maggiore square. It’s a better location if you need parking, or for bus transportation. It was also easier for the Italian Days food tour to pick us up one morning. Perfect location, close to restaurants and shops along Via Massimo D'Azeglio street, but they were completely booked last October, so we found the first place for last year. Looks like they only have the first week of October 2023 available at the moment.

Two years earlier, I had another place, a studio - much smaller, and cheaper. Even though it’s well inside the walls, it’s a longer walk to restaurants. Roberto’s place is https://t.vrbo.io/6p7x4NVQuBb . He seems to have lots of available dates in October.

Staying for a week probably you want to do even day trips to other cities or in the countryside.
In any case my suggestion is to stay close to the center.
If you want to move often by train the northern part of the Medieval center is better: the "slice" from Piazza Maggiore, train station, via Zamboni, via Marconi. If you want to move by car is better stay not very close to the main square (even if the hotel has a garage and you can enter the ZTL) because the streets are very narrow and some days of the week some streets are completely pedestrian. Better stay closer to the external limit of the Medieval center.
I don't know what you like and your budget, but there are two B&B that in my opinion are very special: Torre Prendiparte and Pallazzo di Alcina.