DorthyD- Hank is right on the money here. Do the Vatican first. The guide book is probably written under the assumption that you are staying in Rome and not a cruise passenger. If you are staying and don't have a time line to follow to be back to the ship, then it may make sense to wait until after lunch because by then the cruise line tours will have been through and some may already be gone. BUT as a cruise passenger, if you go as soon as you can in the morning you will probably beat the cruise line tours to the Vatican as it takes them time to organize everyone, bus them down and get them into the place. In fact this is true for all the ports, if you go early enough you can beat the tour crowd there. If you try to wait until after lunch you will have wasted half your day.. and then you may not have enough time and you will feel rushed.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013