Study abroad in florence or rome?

I am looking to study abroad next spring and I cannot decide between Florence and Rome. I want a city that has a vibrant nightlife but is also authentically Italian. I do not speak fluent Italian so this is also a factor. Additionally, I want to travel all over Europe during my semester so which one is more conducive to travel? Overall, which city is more suited to the budget and lifestyle of a student? Any advice would be greatly appreciated!