Given your desire to visit the Amalfi Coast and the fact that you have two weeks, I would spend a week in Rome and a week on the AC, especially if you have not been to the AC before.

I might spend one night away from an apartment I was paying for if it was cheap, but not two or three, thus paying for just a place to store luggage plus a hotel somewhere else. I mean, how cheap could the apartment be? Even if only $100 a night, add that to whatever a hotel would cost for a couple of nights and it is no longer so cheap. I sure as heck would not pay $100 a night to store luggage. With that money, you could buy stuff there. Try to get your DH to learn to pack lighter & plan on doing laundry once perhaps.

We rented an awesome apartment this fall, email me if you would like info. We did a few day trips which were very easy but did not trip out of Rome for overnights. Seems like a waste since there is so much to see and do in Rome. I'm with Sassafrass, perhaps a full week in Rome and a week somewhere else. We spent 17 days in Rome and could do that again and again for the next 10 years and not even scratch the surface of what there is to see and do. Sadly my pesky job has interferred with the trip report.........

The Amalfi Coast is quite a haul. I, too, would suggest you divide your time.

You'll likely land in Rome early in the AM. I suggest you at least consider immediately making your way to an Amalfi base town for 3 nights and then spend the remainder in Rome.

Then you'll have lots of options for EASY day trips from Rome via the main train station (or not, as Rome itself has endless offerings).

After getting sticker shock at hotel prices in Rome, 3 of us rented an apartment in Trastevere for two weeks through romecityapartments. The photos of our apartment were true to life. We loved being a block from the pedestrian bridge, near a bakery and many restaurants, around the corner from an English language bookstore.
We were happy with that location, used public buses, especially #116 across the river.
Enjoy!

thanks for your replies. we have rented the apt for 10 days and will stay local, or day trips. thanks for advice!

Great you have the 10 day apartment in Trastevere and I actually think 2 nights in the Amalfi is a brilliant idea if the weather is nice and the ferry schedules cooperate. I think I might take a train to Naples, a cab to the docks and take the ferry to Capri. Spend a night there, and then take the last ferry the next day to the Amalfi coast in time for sunset in Positano. Goof around the next day, but ultimately take the bus to Sorrento and make your way back to Rome.

PS: When you research day trips, don't forget that there are some buses and trains leaving from the Trastevere side of Rome to places like Tarquinia and Lago Bracciano. Most of the suggestions for day trips you find in guides are based on the idea that you will leave from Termini Station, but there are good buses that go in all directions that are closer to Trastever.

That reminds me that there is a regular bus from Rome to Sorrento if you decide you'd like to see the Amalfi coast but don't care if you see Capri. You can take the bus to Sorrento in about 2 hours and then take a ferry or bus to Positano. (The road between Sorrento and Positano is the most spectacular section of the Amalfi drive.)