Florence: pros/cons staying in Oltrarno area vs near Duomo

If you stay the 4 nights in Florence (as I would) you'll have at least 3 full days in Florence, one of which you can take a day trip to Siena.
If you split your stay into two nights each, you'll be losing a day for the hotel transfer process. If you want to see Siena in the evening, you can take the train back. The last one departs Siena at 21:26.

Oltrarno pros: slightly quieter and also cheaper (both accommodations and eateries). More similar to Florence before the tourist invasion. although Oltrarno has been discovered too nowadays (but there are still quieter spots, if you stay a bit away from Ponte Vecchio.
Oltrarno cons: slightly longer walk to get to most of the sights, which are on the other side of the river.

Duomo area pros: Closer to sights.
Duomo area cons: Disneyland crowds environment in most places.

My pros and cons would be very similar to Roberto's
Oltrarno could be right next to the River or back up the hill so would be different cons depending which.

Duomo: closer to most sites, closer to the train station, in the middle of a thriving area, vast food options at your doorstep, nice mid-day to be close to go back and grab something, take a quick rest, use the bathroom, etc... Also very crowded at most all times.

Oltrarno: Quieter, there are areas of beautiful gardens so can be non-city like in some areas away from the walls, you may have a much better view, could be a walk up a steep hill to get back from the sites in town, due to location and hilly terrain you may not want to make the walk more than once per day so likely need to stay in town away from lodging all day, you are closer to Piazzale Michelangelo which is the place to view the skyline and great at sunset, closer to San Miniato al Monte church which is also nice. Some lodging is cheaper here but not all, there are some luxury places with a view. Nearby food will likely cost you less. You may have parking included where by the duomo will definitely not.

Most I think would choose the Oltrarno for 1 of 4 reasons: 1.) Get away from the crowds / 2.) They need parking / 3.) View / 4.) Cost (though not always cheaper)

Unless you really wanted to be in Siena after dark or at sunrise, I would stay 4 nights all in Florence and take 1 day out of that time to do an all day trip to Siena. Siena will feel less crowded than Florence.

I would recommend either 3 nights in Florence and 1 night in Siena OR 4 nights in Florence with day trip to Siena. It rained when we were in Siena - so, we didn't get to enjoy Siena after dark. But, it didn't bother us. One night in Siena is sufficient. Don't think twice about packing/unpacking for one night. It's easy to get to Siena from Florence - so, you will get adequate time in Siena with just one night.
Picking a neighborhood in Florence depends on several factors. budget, ability to walk with your luggage, arrival by train or car, sights you want to see, type of hotel. If you are arriving by train - I suggest staying around Santa Maria Novella or Piazza Della Republica area. I like Hotel Pendini. But, there's lots of places to stay in Florence and many will chime in.

I love being in Siena after dark, but I wouldn't want to have a full-on move for one night.

I live near the entrance of the Giardini di Boboli, which are in oltrarno. It is about 1 mile from the station, it's a 15 min walk. so I find it indeed very central and at the same Time quieter than near the Duomo. It is not at all hilly where I am.
I like very much the workshops of all kinds (shoes, jewelry, clothes, restoration of furniture, books or painting). The atmosphere is more authentic.

I was just in Italy a few weeks ago. Florence is a solid three full day city, and even then you are leaving things on the table that you will need to see on a return visit. I have been to Florence on each of my four trips to Italy, and this last time was the only one where I spent four nights (three full days). I ran myself pretty hard but still did not have time to do everything that I would have liked. I saw some of things I have seem on prior trips, and missed others, but also saw some new things. I am sure you will have a great time.

My first time in Florence with our family we loved staying city center with all the excitement for our first visit. Now I prefer to stay in the Oltrarno further away from all of that. On one trip I went to Siena for one night but I should've just gone for the day. Florence is my favorite city and I try to go for at least one day each trip that I make. Venice is the most unique city to me but also my least favorite (I know so different than everyone else). Loved seeing it (two times) but have no desire to go back.

Thanks for all the great information, this is so helpful! I know this is probably strange, but one of the reasons I've been trying to figure out what to do with a Florence stop is that my husband and I aren't really art museum people and of course those are the first things you read about in Florence. Friends have told me they aren't either and loved Florence so that's why I started looking more closely. Right now I'm interested in the Pitti Palace and Boboli Gardens, Duomo, San Miniato church, and maybe taking a walking tour as we like to hear about history. And considering that there are good day trips nearby, 4 nights would give us the chance of seeing something else if Florence ends up not being our cup of tea. (Although I think even with what I listed, the 3 days including Siena would probably take care of those sights, and also a chance to walk around as well.) Well, choices aren't a bad thing!

We stayed here recently in the hilly area of the Oltrarno
Amazing view!!!
Walk back from town a bit of a haul up a steep hill but easy walk to San Miniato, close enough that you hear the bells from this church.
https://www.airbnb.com/rooms/567646
More of a B&B than an apartment, grounds are lovely, very quiet with flowers all around and hosts very generous. Great breakfast included.
Private balcony just off the bedroom is huge with a dining table for eating in and a million dollar view, it could use a cleaning outside though.
It may work for you, we had a car and wanted a view which is why we choose it. With a rental car it was easy to drive to Siena for a full day trip and not have to worry about a schedule. but otherwise the car will sit dormant while in Florence.

While in Florence, since you mentioned an interest in history, can I suggest this tour: The women's gallery of the baptistery. (https://www.museumflorence.com/guided-tours/2-thematic-tours). We thoroughly enjoyed it (turns out we were the only two on the tour that day and this made it even more special). Learned SO much about the history of Florence, told in an engaging and interesting way. Highly recommend!

We have been to Florence many times and stayed centrally and the Oltrarno and even past Porta Romana. There is no con to Oltrarno especially fairly near the river. It is a tiny town and it is easy to stroll across the Ponte Vecchio right into the center while having the relatively quieter nights in the Oltrarno. You also are less subjected to the huge hoards of often drunk American college students that fill every street in the center during much of tourist season. It is not far away. It is much less touristy and much quieter; there are lots of good restaurants. All good.

I've been to Florence many times, and definitely prefer to stay in the Oltrarno area rather then anywhere near the Duomo.
That area, and for a few streets near it, seems to be filled with drunken students at night and into the early hours of every morning. It's a nightmare if you have trouble sleeping.
That said, staying near the Station on the side away from the Duomo was quite quiet!
Wherever you end up staying, make sure it faces the back of the building, to minimize any noise.
You are sometimes rewarded with a view into someone's garden that way, so an added bonus!
Have a lovely time, Florence is a wonderful town , if you can look past the crowds.
I would leave Siena for another trip, as there is much to do in Florence, even without going to the museums.

Wherever you decide to stay, a few hours in Fiesole, a local bus ride from Firenze, might be something you would enjoy. Lots of history.

Thanks again for all the continued thoughtful information! Francoisdegrelle, one of the hotels we are considering is La Scaletta, which I believe is very near the Boboli Gardens and seems it wouldn't be a very far walk across the river either.

At first I thought I might want a car for parts of this trip. We've never lived anywhere that has significant mass transit so train and bus schedules are a little intimidating. But I'm now leaning towards mass transit the whole way and hoping for the best!

I recommend La Scaletta. Their rooftop restaurant has breathtaking views too.
Via de Guicciardini is very busy street with foot traffic (cars aren't allowed) but it's quiet at night.
Given where you want to go, the Oltrarno is the best choice.
Cars are not an option in the city center of Florence, including the Oltrarno. Only residents with special permit can drive a car in the historical center (and not even everywhere), so if you rent a car you would need to keep it parked in a public garage the whole time (at very expensive rates). Street parking is not allowed either, in nearly all streets.