Rome is bloody awesome, you won’t be disappointed.
In terms of booking, certainly for city breaks, I find booked independently much better, Rome is very easy to do this. Cheap flight (make sure you fly into Fiumicino airport), board the Leonardo express that is a straight train from the airport to Termini, the main Rome station, then head to hotel either via foot (Rome is a great city to walk around), underground (there are only 3 Metro lines so it is astonishingly easy to navigate) or taxi (not cheap but hey, it’s your anniversary, treat yourself).
And make sure you eat at a restaurant called Dell’Omo. It looks rough as a very rough thing and is tucked away in a corner by Termini, I guarantee you will talk past it twice muttering “it’s can’t be there, not even a random bloke from a forum would recommend that kind of place”. But it is there and once you get in you will be able to partake in some top class, traditional Italian food, no frills, no poshness, just cracking home made food. Oh, and it’s dirt cheap as well. Winner.