Visiting the capital of Tuscany doesn’t have to cost a packet.
The city is so attractive that simply wandering around enjoying the views is pretty much the main activity for visitors. The centre is small enough that most people can enjoy a week without worrying about having to take a taxi or bus anywhere.
Florence does charge for museums but you invariably find combined tickets such as the one that gets you in to the Boboli Gardens, the Silver Museum, Costume Gallery, Porcelain Museum and Bardini Gardens all for about eight Euros.
Eating is surprisingly cheap if you stay out of the obvious tourist traps and eat as the Italians do. Seek out the traditional fiaschetterias where they serve simple food in simple surroundings. Some of these places have been open for 50 years or more and a few (such as Marios on the otherwise best avoided Mercato Centrale square behind the food market) have become semi-legendary for amazing meals at basic prices.
Accomodation can eat into a budget, but there are plenty of smaller hotels on the south of the Arno a few minutes walk from the tourism centre that will delight you both for the quality, warmth of welcome and price.
Flights are no longer the big ticket items they once were, provided that you book well in advance and are prepared for a little discomfort in a crowded budget jet for about an hour and a half. Trust me, Florence is worth it.