Where to stay in Florence? The hills or in town?

Hi, not up in the hills but at the base, we spent 3 nights at the Hotel Silla while on a Rick Steves tour. I enjoyed the hotel, the breakfast, their terrace, and the overall location.

If you're not in the city, you'll need a car. For Fiesole, for instance, its a few buses' connection.

We stayed outside the old town and had to take an expensive cab each way. Also, once we went back to the hotel we didn’t return in the evening for a nice stroll or gelato.
We only stayed outside cause we get an employee discount at the Hilton’s. I would pay the higher price to stay closer to the middle but hubby likes his deep discounts. Many times I am secretly happy when there are no Hiltons available.

If by "the hills south of the city" you mean the Oltrarno area just across the Ponte Vecchio from the city center then it's pretty straightforward - lots of nice places to stay over there. We usually start at Booking .com to research places and sort out locations, then see if a place has it's own website for a direct booking ... and maybe a better deal.
If you're thinking a bit further afield then I'd suggest looking at a map of the local bus system which is a cheap and efficient way to get around if you don't want to be springing for a taxi every time you go out.

We stayed at Hotel David which is a 20 minute walk along the river or a bus stop right there to get to the main area. It was very convenient and right on the river and in a neighborhood with restaurants. I liked being able to head out on foot easily. While the street in front was busy the hotel was quiet.

I’ve stayed in the Porta Romana area (a few minutes walk beyond the Boboli Garden) a couple of times and been very happy. It feels far more neighborhoody to me.

Can you remember wher in Porta Romana you stayed?

Yes, I’ve stayed in the same Airbnb twice and will probably get there again at the holidays. I rent a room with private bath from a wonderful retired chef. The view from “my” room looks out to the Duomo and mountains. I can’t imagine staying anywhere else, but it’s probably not everyone’s cup of tea. To me, it’s more of a traditional B&B, but with kitchen privileges rather than an actual breakfast provided. If you’re interested in the specific listing, I’m happy to share it with you.