First of all, congratulations!
It's a good thing that you're getting an early start on planning. As this is your first trip to Italy, you'll need to get up-to-speed on the specifics of travel there, which include some potentially expensive "pitfalls". My first suggestions would be to read Europe Through The Back Door and then pick up a copy of the RS Italy guidebook. Those will provide you with a lot of good information to help your trip go smoothly.
I agree with the others that it would have been preferable to use "open jaw" flights as that's more efficient and allows you to maximize sightseeing time. Does your time frame include your two flights days? It would help to have some idea on where you're flying from, as forum members in your area may be able to provide some good tips. Also, what time does your flight arrive in Rome? Limiting your trip to three destinations with some day trips would be ideal.
I also most definitely agree that it would be a good idea to skip Milan. While it does have some interesting sights, IMHO your very short travel time would be better spent elsewhere. As you don't seem to have much interest in Venice, I'd suggest arranging your Itinerary as a "loop". When you land in Rome, don't stop there but immediately go to your first destination (Florence?). That's going to make for a long travel day after a long international flight, but a more efficient method.
Someone else mentioned the Cinque Terre, so I was also going to suggest that you have a look at that. While it can be crowded at times, that would be a great area to spend a few days while recovering from jet lag. If you decide that might like a few days there, you'll have to decide which of the five towns you want to stay in. The C.T. is a good possibility as it's easy to do a Rome > C.T. > Florence > Rome loop. While in Florence, you could also take day trips to Siena (by Bus) or Lucca, as those are both easy. Venice is also possible as a day trip, although it will be a "longer" day trip due to the travel times involved.
Good luck with your planning!