Good food abounds in Florence but ignore street food and pizza stands (these are better in Rome) and eat plenty of Gelatto. The best course to find inexpensive, authentic, and delicious Tuscan food is to ask a local who speaks English where he goes for lunch or dinner (be sure to mention that you aren't interested in where the tourists go.).
Leather is a great bargain in Florence but be careful of shoddy workmanship on street stands. Have fun haggling for something; it's part of the great experience of Florence. Leather briefcases are often a good buy here. Shop around for the best price. Learn to say no and watch the prices drop.
The nightlife in Florence is active, what with the many universities and the presence of young tourists from around the world. One of the best scenes is near Uffizi gallery, where an impromptu night market sets up, at least until the police arrive. Lots of lound World Beat music and lots of fun. Nothing is as breathtaking is happening upon the statue garden near Uffizi late at night.
For meat lovers, the best steaks in the world can be found in Florence, the Tuscan cut--perhaps a little leatherier than in the U.S.--but seasoned with a delicious blend of spices. In most places you will buy a huge slab and have it delivered to the table where diners can carve off as much as they want.
If you are daring, you can bargain for your hotel rooms once you arrive in Florence, especially if you go by train. We spent about $18 a night for so-so rooms with common bathrooms (shared). OK to collapse into but not a place if you want to spend extra time sleeping. In most European cities, it is customary to look over your room before agreeing to check in for the night. Do it. It will save you much heartache.