Yes, you can. Do not even think about driving....I would agree that heading right to Florence upon arrival in Rome and BUY ticktes on the spot....just stay 2 nights...( Day ONE & TWO) it is a small walkable city...you should stay in the historical center of Florence ( and Rome it is worth the extra money for the short time you have, you will only have to walk 10-15 min between major sights and take train to Coloseum very easy)....you also may want to be sure that the hotel can hold your luggage in Florence upon arrival/or store at train station until you can check in...travel light a rolling 22" and a small day bag is all you need! (Day THREE morning, or afternoon) Go back to Rome by train...check into your hotel and go for dinner...maybe walk to Trevi Fountain after dinner when crowds are a bit smaller....see Rome 3 nights. (Day Three night ,four and five)..go to Naples for THE DAY ON DAY SIX arrive by 10 am if you can, make sure you are on a fast train 1.5 hours... get a great coffee and pastry near the Garibaldi train station .or head to museum and have a bite to eat before going in....see the Archeological museum if you like, weather permitting go to Herculaneum...25 min ride on train and 1.5 - 2 hours to visit this less crowded, well preserved and smaller sight...compared to Pompeii. Get back to Rome in the late afternoon or early evening of DAY SIX and Seven in Rome fly on day Eight (?) Maybe even stay 2 nights in Florence...unless you are going to Vatican City...this usually warrants 2 trips, two 1/2 day excursions... So 1-2 nights in Florence, 1 day in Naples, rest of time in Rome. I only recommend 2 nights in Florence to help you "get on the time zone" as it is a more compact city compared to Rome and then you will be ready for Rome and Naples! But 1 night is okay...Rome can be " seen" in 2-3 days, but of course you could return for a lifetime! As far as safety, if you are from any big U.S. city, you are streetwise..but always keep 2 or 3 stashes of $ and credit cards. In winter you have the advantage of coats, but if you take it off and $ is in pocket bye bye coat..so money belt and keep a day's cash and one cc in zippered pocket of shirt or deep from pocket of pants. Women should limit amount of valuables in handbags and opt for cross body bag with strong strap and wear it UNDER their coat turned toward them as you will see Italian women do in crowds! Enjoy! I love Naples, but if you are enthralled with Rome, and just want to stay put, see Naples on another trip with Amalfi coast or islands...unless you are interested in the archeological things...