Is it wise to stay in rome and make trips in the morning to florence by train and come back at nights?

I am going to spend a few days in italy and would like to visit rome and florence. I'm flying from paris to rome and my return ticket to LAX is from rome. I dont want to spend one week in rome and would like to see florence as well. I'm just thinking of booking my hotel in rome for the whole week instead of booking another one in florence, since it's kind of hard to carry the suitcases between the two cities. Which one do you think is easier, booking hotels in two cities or geting a hotel in rome and taking 2 or 3 trips to florence every day and coming back at nights? Remember, my return ticket is from rome and I have to eventually come back from florence to rome in order to catch the flight.