College couple spring break in Italy

If you end up staying in Rome, try to get beds at The Beehive Hostel. Clean, safe, and close to the main train station in Rome. Book as soon as possible since it fills up quickly.

You should split your time between Rome and Florence. The Cinque Terre is more of a Summer place.

At that time of year it would probably be best to focus on cities as it could be a bit chilly and wet (ie: Rome and Florence), although that won't provide many "hiking" opportunities.

The Cinque Terre is not the best choice in March as most tourist businesses there don't "officially" open for the season until April 1st (although there will undoubtedly be a few open in March). The Cinque Terre might work out if the weather is favourable, as that would provide some hiking. If you were planning to hike the popular Sentiero Azzurro trails, only two of the four segments may be passable, however there's an extensive network of other trails in that area. There might be a few hotels open in Monterosso, but if not you could stay in Levanto or La Spezia as it's only a few minutes by train from either of those to the C.T.

If you choose Florence, the Archi Rossi hostel is a good choice, barely a 5-minute walk from the train station, another 5 to the sights

4 days in Florence (do a full day wine tour through the Val d'Orcia area and a day trip to Siena)

4 days in Rome (one day of the Vatican, one day of Ancient Rome, two days to just explore)