Open container law:
There is none! not ready to go to the bars or clubs, maybe just want to have a drink and walk around the city at night, go for it ! You may be looked at by locals as the usual tourist but as long as you are not destructive or obnoxious no one will bother you. Grab some beers or a bottle of wine from a local mini market or grocery store and stroll around this beautiful city. have a drink on the steps of the Duomo or go to any Piazza and there is surely some beautiful live music (the final song from step brothers).
Unless there is rain or you have heavy bags there is no real reason to take them. The city is easily walkabout and beautiful don't miss out on it by sitting in the back of a car!
There is plenty of options and 1000's of study abroad students. As long as you find the bar you like you will easily meet fellow travelers and the local students for a great night out! Clubs do not open up until around 1 when the bars begin to close down.
Thieves and Gypsies:
It goes without saying to always watch who is around you and for your belongings but the gypsies in this city are very "good" at what they do. They will try many tricks such as using there children to distract you or putting something in your face asking for money while there hands and grabbing anything your not paying attention to.
Almost anything on Mondays are closed in regards to museums, galleries, and several local restaurants. The bars are still operating and the city is still beautiful none the less but look up the different galleries and museums before visiting here and becoming disappointed because you can not access what you want.
Happy Hour! (Apperitivo)
Very big in Florence usually starting around 4-6 at plenty of cafe's, arrive early to secure a table, buy any drink on the menu and you have free access to the snacks and food they have laid out for there paying customers. An excellent way to start off the night and great if you are not hungry enough for dinner but need some food. Listed in another section are the best locations.
One of the best kept and known secrets of Florence is the magical secret bakery! A place you can only get to if you know where to go or if you can smell the delicious pastries that are being made. "Opens" around 1-2 in the morning and if you do happen to find the door to this place you have to be quite or they will not open and answer for you. Find a local study abroad student and they should be able to bring you there after a long night out.
Yes gelato is an everyday every meal occurrence and not all gelato tastes the same. When studying abroad there we were told very simple rules for looking for gelato. 1) Do not buy it next any of the touristy sites (unless you at the top of Michelangelo's peak and want some) This will be extremely expensive and although good not the authentic gelato you are looking for. 2) Always look for the price of the cups or cones first. We once bought 12 euro gelato because they did not tell us the price and it was buy the Ponte Vecchio. 3) If it is stacked to the top like a mountain that looks pretty and appealing do not go there! Look for the very simple ones that look like there about to run out.