It really all depends on what your interests are, what you really want to experience. For some people 1 day is too long, for others a lifetime is too short.
If you are looking for the traditional picture postcard, guided tour, I have been to Italy kind of trip, then the answers above are fine. If your goal is to also know modern Italy and the Italians then the priorities will change a little. Rome will have the shopping and good restaurants, but you may want to spend time in the less traveled parts of Rome, to eat at the local trattorias to get a feel for typical Italian food and to mix with real Italians.
The same is true for Florence, but there is also the countryside with fabulous scenery, vineyards and wineries not far outside of town. The Arno is a beautiful river. When I was there I watched crews practicing with their racing shells on the Arno, not far from the Ponte Vecchio.
Basically what I am saying is that there is so much more to do than trying to cram in all of the tourist sites of two cities in seven days. Nothing wrong with that, but slowing down, spending the time to see how people are living now as well as seeing the historical sites is more interesting to me, a better experience.
Part of your planning is researching to see if there are any local festivals going on during your planned visit. Only you can decide what your real interests are.
However you plan your trip, have fun and enjoy.