Didn't go on honeymoon to Italy but went as follows:
2 nights Rome
2 nights Florence
3 nights Venice
It was definately the right order for us to do it - we just booked flights to and from and the hotels then got trains when we got there - were very cheap even for first class - especially compared to England! Was about £30 per leg first class at the time.
Venice was amazing and our favourite place now - we were so glad we ended up there and have been back a few times just to Venice since. It's a cliche but it is for a reason - because it's amazing! If you go in 2013 (or every other year after that) you will be there during the Biennale which is a must do - a city wide art exhibition that exhibits in old crumbling palazzo's normally closed to the public and in loads of public spaces.
Stayed in a good hotel right near the Vatican in Rome - Hotel Columbus - rooms were basic but we didnt pay for a better room but think they were available - but the breakfast room was something else! Fresco'd crumbling ceilings...amazing. I like crumbling stuff! The other hotels were ok but the FLorence one was gorgeous but a bit far out and the Venice one...well - if you have the budget use it in Venice as there are a lot of cruddy hotels. And a lot of cruddy restaurants - but you dont go there for the food thankfully
Italy is amazing - have fun