First of all, if you are studying abroad in Florence just know how lucky you are. Appreciate the time you have in one of most beautiful cities on earth. As cliche as it may sound, time truly will fly by. Don't spend your time counting down the days until you go home because once you're home, you'll long for more days exploring the Renaissance city.
With that being said, spend your time wisely. Don't sit in bed all day or go to the same part of the city, wander around the city until you're lost. Wandering will lead you to place, you'd never go otherwise. Discover new places, new restaurants, and new architecture. Discover everything until you know the city like the back of your hand.
Get to know the locals, even if you can't understand the language. Don't just spend your time with Americans, dive into the culture head first. Try to learn Italian, even if it's only a phrase or two. Having relationships with the locals will make your time in Florence that much better. Ask them what their favorite restaurants are, their favorite museums, or even their favorite part of the city. Be friendly and say, "ciao!" to the mini market worker on your street.
Go everywhere and do everything. Don't wait until the last week to start doing the touristy things. Go to the top of the bell tower or the Duomo, watch the sunset from Piazzle Michaelangelou, go inside Uffizi and Galleria, spend time in each piazza. Time will fly by and before you know it you won't have enough time left for everything. Make a list of things to do and starting checking things off.
Spend your money wisely. Spend your money trying new foods, traveling, going inside museums, etc. Dont waste all your money going out to clubs and buying clothes you could buy in the US. In need of an American style breakfast? Head to Le Vespe for the best pancakes, bacon, sausage, and other breakfast foods, or head to Amalo for the best muffins. Try new Cafés until you find the best cappuccino in the city. Eat your weight in gelato, spaghetti, and/or pizza. Spend your money trying new things.
Florence is one of the best cities in the world and when the day comes that you leave to come home, you'll be filled with joy but you'll also be heartbroken. Not knowing when you'll return to the city, will make your heart hurt, so appreciate the time you have. Take everything in around you, drink too much wine, travel until your bank account is empty, see the David, watch the sunset, get the best view of Florence up above, and most importantly have the time of your life. Florence will steal a piece of your heart forever with its beauty and charm. Be thankful every day you get to wake up in the beautiful Italian city, because time will fly and before you know it you'll be back home.