Florence...What to see and where to stay?

With only one day in Florence, there's no need for a day trip outside of Florence. Depending on what else you're planning for your trip, and how much time you have, you could easily spend two full days in Florence. If you are only visiting one museum, then I would suggest the Uffizi, one of the best museums of western art in the world. But then you'd be missing out on visiting David, which is at the Accademia, a much smaller museum with David as by far the main attraction. And you're missing out on the Bargello, a beautiful building housing amazing sculptures. In terms of churches, there are tons: the Duomo; Santa Croce (Michelangelo & Galilio are buried here, among others); Santa Maria Novella (painting by Giotto, among others); the Medici Chapels (sculptures by Michelangelo); San Spirito (more gorgeous from the outside), to name just a couple.

Lexma, we do have 2 full days in Florence (then traveling via Pisa to Cinque Terre). I guess I'm trying to figure out if we should spend both days sightseeing in Florence or if there is anything close by that's worth a day trip.
My husband is not too much into museum (with only/mostly paintings). So I'm trying to figure out if I could do one...which should it be?

I recommend staying at the Hotel Accademia. It is reasonably priced and virtually across the street from the Medici Chapel (which I also recommend visiting). It is also a 10-15 minute walk from the train station at most. Since you husband isn't into paintings, I would skip the Uffizi and head to the Accademia and see David and the Prisoners. This will be a fairly short visit since it's a small museum, but make sure you get a reservation to avoid lines. Other suggestions: Piti Palace and get a picnic together and wander around until you find a nice park to enjoy. There is one directly in front of Santo Spirito Church, which is a really nice church. With only 2 days, I would concentrate on Florence rather than day trips elsewhere.

Congratulations on your trip! You're going to have a great time. When you say 2 full days it's not clear if landing day is one of them or if you have 2 full days after landing day. My experience is that landing day has a lot of housekeeping details, starting with collecting bags, getting euros, finding correct transportation, the hotel, checking in, ping bags, taking a breath and getting a little oriented at the hotel with a city map before heading out for some sightseeing, good food and gelato. (Every town change has some "housekeeping" time loss, though it is usually a lesser issue than after an international flight.) My first trip I traveled with someone who didn't want to do ANY museums, we didn't do many and had the time of our lives. (We did do a lot of churches.) For Day 1, I heartily recommend that you wander, get lost, get your bearings, laugh, get some gelato and get lost again, all the while taking in the sights, sounds and flavors of Florence. If Day 1 is landing day, stroll the city, take in some of the great markets in Florence, admire the Duomo, maybe climb the Dome and enjoy the city vista. Watch the sunset over the Arno from a bridge or maybe take in an evening Mass at San Miniato when the monks sing Gregorian Chants. Ride the merry-go-round. Most well known markets: Ponte Vecchio collection of specialty and gold & silver shops San Lorenzo Market Sant'Ambrogio Mercato Nuovo covered and known for its wild boar statue
Mercato Centrale or Central Market If you want to do a "side trip" outside Florence, I'd consider an organized half day tour that leaves and returns to Florence or take the 30 minute bus ride up to Fiesole. I recommend B&B Badia http://www.badiafiorentina.com/?act=home as a good budget accommodation in Florence. Bruno is terrific and the accommodations are clean, central, and comfortable.

Astrid, although I'd hate to miss the Uffizi, if your husband's not too excited about museums, you might consider a short visit to one of the smaller/less crowded museums. The Bargello is a great collection of sculpture in a historically interesting building; the convent of San Marco has the world's best collection of Fra Angelico's work in a lovely convent that was one of the first Medici projects in Florence; the Pietre Dure museum has a collection of remarkable Renaissance mosaic work, along with a display of the stone-working equipment used; and the Palazzo Davanzati is the 14th C home of a wealthy merchant family that provides an interesting view into life at that time. If you enjoy churches, I second the recommendation for San Miniato al Monte. It's often described as one of the most beautiful Romanesque churches in Italy and provides a lovely view over Florence (particuarly at sunset). Most of the interior dates from the 13-15th C. There's a beautiful fresco of the life of St Benedict in the sacristy, and a stunning apse mosaic. FYI, the Gregorian chant in the evening is not Mass, it's Vespers (although there is a Mass after Vespers, often in a different portion of the crypt). I also love the cloister of Santa Maria Novella (which keeps shorter hours than the church); it's usually a quiet escape from the city. And the former pharmacy of Santa Maria Novella is an interesting visit; it now sells various high-end creams/fragrances/etc; it's on a side street about a block from the church. If you want to do a day trip, it depends on your interests. Most people like Siena (an hour or so by bus), but I much prefer Assisi (a couple of hours by train). Assisi is a really well preserved town, while Siena has a much larger modern section. Also, Fiesole is a pleasant short trip outside of Florence.

Hello Astrid, If you go online for the Accademia museum, you can make a reservation which you can print out and take with you. Just google Accademia Museum. With that, you get to skip the long line, and getting into the museum only takes a few minutes. Michaelangelo's David is the main feature. If you so wish, you can spend the time you want to study this magnificent sculpture and then be off. I think both you and your husband will enjoy having spent an hour or maybe a little longer seeing one of the most spectacular sculptures of all time. Seeing it up close in person is spellbinding. If you decide to go to the Ufizzi, you can get reservations ahead and avoid those long waits too.
If you like science and want something out of the ordinary, the science museum is very interesting. They even have Galeleo's middle finger on display -- really. Lots of inventions, machines, etc. Florence is quite compact, so you will see a lot in 2 days. It is enjoyable just to walk around, but be sure to go in the churches, etc. And eat your fair share or more of gelato!

We stayed at the Relais Hotel Centrale. It was centrally located, we could walk to everything, including the train station. Price was reasonable as well. We stayed two days for just Florence and that was tight. I don't know what your budget is but we took tours with ARTVIVA. It was a little price but I was very glad in the end. My husband is not into looking at pictures on the wall either. The guides were so well educated about the information and brought it right down to our level. In the end, my husband told the guide she made art fun, he even enjoyed it. The other advantage of taking the tours, they hit the most important items. Uffizi is massive. We took, the walking tour of Florence, Uffizi Gallery and The Original David. You can do it in one day but I would break it into two.
If want to chose between the three, I would go with Uffizi, Walking Tour, David.

Do a search online for Florence's top 10 and decide. Two days in Florence aren't enough to also venture outside. It's not even enough for Florence alone.

I've done a couple of tours with ARTVIVA as well and highly recommend them. I did a fabulous evening Renaissance tour/walk that ended with olive oil and wine tastings. Great guides and really fun informative tours.