Arrive a day or two early and stay a day or two after. That let's you really explore. Our latest Med sailing was Barcelona-Venice. Plenty of things to do at both ends to justify staying longer.
As others have said, it's very port intensive with
lots of walking. I actually lost a bit over 5 pounds on that Med sailing despite all the food I ate. Get really good, comfy shoes.
Use
DCL to book excursions. Traffic in major cities like Rome is horrendous. Our Rome excursion was
way late getting back to the ship due to traffic, but it waited for us and many other excursions since our guide called ahead and made sure we weren't left behind. After we boarded and got moving, we saw other buses and taxi's pull up at the port, but it was too late for them. If they booked DCL, the ship would either wait or DCL would get you to the next port.
Also, if the port is having bad weather and excursions get cancelled, booking through DCL makes getting refunds and booking other excursions very easy. Don't think it would be too easy with other vendors. DCL may cost more, but the peace of mind when unexpected things happen was worth it in my experience.