In Florence in October, Couple needs 1 bedroom WITH terrace or balcony

I have not stayed at those two properties, but see no downside to the book listings. Since one doesn't serve breakfast and the other offers kitchen access, you'd be able to have your own food on the shared terraces. I assume you saw that the second has no elevator.

Thanks, Laura.

The Hotel Il Bargellino looks like a nice large terrace.
Is it a little distant from some of the central sights?
And how noisy and safe is that neighborhood?

Anyone have other suggestions?

I’ve stayed at Il Bargellino several times and really like it. They have 3 rooms with direct access to a large shared terrace, 2 with private bath and 1 with shared bath as I recall. The terrace rooms are pretty quiet at night, although there’s sometimes a little bit of evening noise from others using the terrace. While the location is away from the center, walks aren’t terribly long. For example (and depending on how fast you walk), the train station and Central Market are about 5-10 minutes away, the Duomo and Accademia around 10-15 minutes, and the Uffizi and Ponte Vecchio maybe 15-20 minutes. Note that they don’t serve breakfast, but some rooms have a coffee machine (similar to a Kuerig).

I stayed at B&B Il Bargello about 5 years ago. It’s a block from the Bargello museum, so more central. It’s on the top floor, which I believe is the fifth floor, so lots of stairs. There’s a small terrace on the roof (picture on their website), which is accessed by a spiral staircase. None of the rooms have direct access to the terrace.

Palazzo Uguccioni on the Piazza della Signoria. We stayed in the Alcove, the studio apartment, with small kitchen/living room, and the bedroom was a separate area.
Balcony/terrace - small but pretty with flowers, and a small table and chairs. The view is rooftops, and you look up over the roofs to the tower of the Palazzo Vecchio. Beautiful to see it lit at night. We listened to the bells ring as we had dinner al fresco.

Although right on the piazza, it was absolutely quiet.
Perfect location, everything to see was 5 to 15 minutes walk away. We stayed there for 5 days.
We booked on booking.com, but you can also contact them directly.

The location of Palazzo Uguccioni sounds great. I went to their website. Here're the photos of the Alcove apt. The terrace is pretty tiny. http://www.palazzouguccioni.com/apartments/alcova.html Most of the reviews on TripAdvisor were positives, but there was one that had reservations about the only exit was the elevator.
If you scroll down and read the thread Affordable Florence-Anyone stayed at these places?, there are a couple of entries about Hotel Il Bargellino. Their terrace is definitely larger.

FYI - besides the private elevator (key access), there is a staircase, so no safety issues there.
The terrace is small, but plenty of room to dine outside (and hang clothes to dry!) We found that after staying in BnBs for 10 days, the apartment gave us room to really stretch out and relax, esp. appreciated since we were staying 5 days. Truly enjoyed staying there, but I'm sure there are many other options in Florence.

Thanks for the comments.

The location of Palazzo Uguccioni sounds great. I went to their website.
Not available for our dates.

Any other suggestions?

Don't just go by the hotel's website for availability. Email the hotel directly (of course, start looking for other places as well). I just made reservations for my upcoming Swiss trip, and in several cases got rooms via email that did not show on either the hotel's own booking site or on other sites like Hotels dot com.

I stayed at Relais Grand Tour in one of their three suites with shared terrace and it was delightful. RS-recommended, it is about a ten-minute walk north of the Duomo.
Cynthia

A lot of hotels will require smokers to go completely outside the hotel, and not permit smoking on terraces, if that is a concern.