Must dos or suggestions please?

Stop by the Orsanmichele while you're there. There are some nice frescos and a beautiful tabernacle. There's also a ticket booth on the back of the building where you can buy tickets for the Uffizi, Accademia and other museums. There are rarely any people in line there while the lines to get into the museums can be an hour or more. When I went by on Saturday, there was no wait at the Orsanmichele ticket office - it's between the Duomo and Palazzo Vecchio just a couple of minutes walk from the Uffizi.

Go up to Piazza Michelangelo for the postcard views of the city. While you're there continue up the hill to San Miniato al Monte. There are good frescos in the church and a nice small shop run by the monks. The walk either up or back down through the rose garden is nice.

The suggestion to see Fiesole that someone else gave you is good.

When you go to Pisa, go early in the day. See the tower, duomo, baptistry and cemetary. Then hop back on the train for another 25 minute ride to Lucca for the rest of the day. There's a lot to see and do in the old walled part of the town. There are a couple of towers that you can climb. The Torre delle Ore is a good choice because you can get some great pictures there and include the Guinigi Tower with the trees growing from the top in the photo.

As to foods to try - the Ribollita is typical of the region. There are different styles at different restaurants. I went for lunch last Saturday specifically to get the Ribollita. Cinghiale (wild boar) is also good. Florence is famous for Fiorentina if you like steak. For dessert, try the cantucci & vin Santo. There are a lot of other typical dishes that are possibilities.

Well, get a guidebook and go to the major sites.

I also suggest you get a bus (if I remember rightly I think no. 7) up to a little town called Fiesole in one of the hills. It is a really beautiful town and there is a lovely Roman amphitheatre, baths and temple (which not many people know about!)

Lucco is also a nice place - you can get a train from Florence station in about one hour.

As for food, in the centre of Florence you may find some of it expensive. I suggest you look around for small, family run restaurants that are off the main streets. Trattorias will be better than restaurants (cheaper and more friendly/relaxed).

Never been to Pisa, but I know you can get a train from Florence. Speaking to people you have been I think the only thing to do is see the tower.

Hope you have a good time, it really is a beautiful place.

Hanging out in Florence will be easy as it is big and fun.

Pisa is 50 minutes by train and will get very boring after you visit the tower.

If you are young you might find some fun in students places downtown, otherwise better take the train back to Florence.