I have tried to write this review for other like-minded people (so art lovers please don't be offended!).
If you are not interested in sites like the Uffizi or the Duomo, then just pass them by as we did. Yes they are pretty, but also to me pretty boring. We did try a bit of culture and visited the Gardens of Boboli, but unfortunately did not find these to be that well kept. The lawns were patchy and the hedges not very well cut. It may be because we were out of season, (we were not charged for entry).
The city of Florence is full of narrow winding streets to explore, it is pretty small, so there is no danger of getting lost, just turn right a couple of times and you always seem to be back in the place you started from!
The narrow streets are full of shops, lots of leather shops, too many to be honest, it would have been nice to have had a bigger variety to visit. They all have their siestas around lunch time and don't open again until approx 4 to 5pm. I am surprised by this, as there are so many tourists, I would have thought they would have taken advantage of this and remained open.
The big shopping stores are just off the main square and are much more commercialised with a couple of department stores and the more well known clothing stores. We went there late pm and it was very busy and had a good atmosphere, so was a good place to amble about.
I am not sure if these shops close in the afternoon as we did not visit at this time of day but I would not have thought so.
If you like people watching, then do this from the cafes in the main square, Palazzo Della Signoria. The Caffè Rivoire is the place to try if you like hot chocolate. It is so rich and thick, I really think they simply melt a slab of the stuff and pour it into your cup! We also enjoyed pre-dinner drinks in this cafe and people watched to our hearts content.
If you are looking for ice cream, Rough Guide.com recommends Vivoli (Via Isola delle Stinche 7r.) as the best ice cream in Florence. I don't know if it is the best, but it certainly is very nice, much richer than some others we tried. Don't bother with the rest of their food though, very basic although cheap.
When it comes to eating, I was a little disappointed with the food (although to be fair I was only there for a couple of days and may not have found the best places to go). Florence charges seperately for all of it's dishes, so what seems inexpensive can suddenly be more so, once you have added all your veggies on. The best place we found was Gusto Leo's behind the main square, full of italians which we think is always a good sign!
I can't tell you much about the night life as we did not do it! We spent our evenings in the restaurants. But there are plenty of young people around and from the noise and laughter coming from the streets in the early hours of the morning, I imagine the night life is plentiful!
In all Florence for non art lovers is a good place to visit but I would recommend only for a couple of days, we did part city break and then went onto a beach resort to finish off the week.