Hi,
I'm stationed in Naples. While not a subject matter expert, I've been to Rome twice now. Both times I used cross-pollinate.com to find a place to stay. This is a coop of B&B's and apartments for rent. I recommend an apartment because of privacy - nice to have on an anniversary, and because if you want, you can pick up some food at a market or paticceria (also called tavola calda, or gastronomia) to bring back a meal to eat. This is the cheapest way to eat. Note, there are apartments that charge per person for breakfast. Don't do this. The Italian breakfast consists of the equivalent of a danish and a cappuccino. It's cheaper, about half, to just go to a bar and get it there.
There is an excellent, mouth watering, fun paticceria we've been too each visit and will go back every-time. It's called Forno Roscioli. Find it at www.fornoroscioli.it, Via Buonarroti 46/48. It's right off Piazza Vittorio Emanuele. Trust me, don't miss it!! Plus as a bonus they always had one person behind the counter that spoke good English.
We've been to some of the biggies- coliseum, forum, palatine hill, St. Peters, and the Vatican museum. If you are going to be in Rome for 3 days, on the first day, buy the Rome pass, 20E per pass. This gets you in the first three on my list above (+ discounts @ others) and gives you unlimited access to the buses and subway for 3 days. This pass is only worth it if you use the public transportation for at least 2 days.
St. Peter's is free. Get there early to get in line for security. Once through there you'll have as much time as you want. Make sure you either bring food in a back pack for afterward or leave the Vatican city area to buy lunch. Nothing is reasonably priced there and the food isn't any different than anywhere else in Rome that I could tell. To climb the 500+ steps to the top of the cupola it's only a few euro ea. It's more if you take the elevator (it only goes 1/2 way). Everyone takes the elevator going down. Definitely do this - it was a fun climb and an excellent view not only of the Vatican city but of Rome.
If you go to the Vatican museum you need to prioritize what you want to see. If your goal is the Sistine chapel and you only have a couple of hours, it'll take that whole time to just walk through the museum to get to it. Why? Because there is such a HUGE amount of very cool stuff to look at on the way and the chapel it's self will take awhile to take in. If you want to see the whole museum, plan a whole day for it. You'll need it.
The other sights people check off their "list" is the pantheon, spanish steps & trevi fountain. These are all within walking distance of each other. So pick a metro stop near there and walk the rest.
Some people really like walking. If you're on that list, the historical center of Rome really isn't that big and you can walk everywhere with the exception of the Vatican, you'll need the metro for that. If you do plan on walking, then skip the Rome pass and just get in line for tickets.
You can rent English audio guides at most places or bring a good guide book. Don't get sucked into the many freelance guides pestering you for work. We use Rick Steve's guide. It's the perfect amount of history for us and it's fun to follow his self guided tours in the book and read to one-another. Don't be surprised if one of those freelancers tells you how bad that book is. To me that's the perfect endorsement; the book is taking away their business.
I just read some other responses and they have some good points. Although, when coming from Naples, the Rome train station is quite nice and very clean in comparison. :) We did Rome with 3 kids too and they did all the walking. As long as you have enough snacks and enough rest stops they'll get along fine.
Some standard safety tips: Remember to always carry TP, wipes, and clorox wipes. You never know what condition the WC's will be in. Be ready for a squatter in the floor and there is rarely a toilet seat. Keep most of your cash and all ID's in a neck carrier inside your clothes. Keep nothing in your back-pack that can't be replaced. When walking or using transportation always have your bags across your body, on your front with one hand on. These simple things advertise you're not a target and you won't have any trouble. Never, never help someone with their "dropped" items on public transportation. They can pick it up themselves.
You'll have a great time; I know it!
K.