I've been to Rome several times, including a week for my honeymoon.
First off, let me congratulate you on your upcoming wedding. Congratulations! You've also picked a beautiful place to go on your honeymoon. You can't beat the Eternal City.
There are many many things to do in Rome, with the following list being some of the most common and popular choices.
St Peter's
Even if you're not Catholic, I recommend visiting St Peter's Cathedral. It really is amazing. The size is of the dome is staggering. Even though I'm an atheist, I found the serenity in their palpapable (if you'll allow me an oxymoron).
The Forum
I'm absolutely fascinated by Roman history, but I think everyone would enjoy this visit. You can see the Curia where the Senate met (rebuilt by Mussolini, but very accurate). It's much smaller than you may think. There's also the many many temples and Fora (or markets) to be explored. You can actually see the remains of the Temple of Juilius Ceaser, built on the spot where his body was cremated by the people of Rome after his assassination. To this day each morning fresh flowers are left at this location.
As you walk down from the Capitoline Hill (see below) you travel along the Via Sacre (or Sacred Way), towards the Colosseum.
Colosseum
It's truly amazing to think that this was built almost 2000 years ago. It's accurate name is the Flavian Amphitheater and is only known as the Colloseum, not due to its size (a common misconception), but because it was situated near a huge gold statue of Nero called the Colossus. It was built to hold 50,000 spectators and has 12 different entrances, each one providing access to particular Roman citizens depending upon their "ticket".
Circus Maximus
Just down the road from the Colesseum are the remains of the Circus Maximus. This is a huge racing track immortalized in the movie Ben Hur. Remember the chariot racing scene? That was set in the Circus Maximus. Overlooking the Circus Maximus are the remains of the great Imperial Palace (on top of the Palitine Hill), where the Emperors could sometimes watch the activities below them.
Capitoline Hill
This is the religious heart of ancient Rome. This overlooks the Forum and is not far from the Palitine Hill. From here you can walk down to the Forum. Actually, it's a good starting point for your exploration of ancient Rome.
Palintine Hill
This abutts onto the Forum and is where the richest people, and later the Emperors, built their houses and palaces. Climbing up towards the Palitine Hill from the Forum gives you a great view of the Colesseum and the ruins below you. Truly amazing.
Forum Augustus
This was originally part of the Forum, but is now on the other side of a large major road built by Mussolini. You can walk back along this as your return from the Colisseum. This is also where Augustus built the very impressive Temple of Mars the Avenger (
Martius Ultor I think). Actually, all along this road are very impressive temples and ruins, including the Forum of Ceaser (opposite the Forum of Augustus).
Vatican Museum
One of the best museums in the world. Truly breathtaking collection of materials from Etruscan times (the people "before" the Romans) all the way up to modern times. Lots of paintings if you're into your art, including numerous masterpieces. Make sure to see the Sistine Chapel (though officially this is in the Vatican proper, and not the museum). Recently restored, it is well worth the visit. Remember this is a living place of worship, so be respectful.
Catacombs of Rome
These dot the underground of Rome and are pretty spooky. It's where the original Christians used to bury their dead, and were used up until quiet recent times (even during WWII by partisans and anti-Nazi agitators). Still stacked with thousands of skeletons, it really is an experience to take a tour.
Back streets of Rome
Make sure to step off the main trail and wander some of the many many small, winding back streets of Rome. Make sure to eat here in any of the hundreds of small family run trattroria and cafes. Stay away from the large and very expensive tourist restaurants. You will need some pidgin Italian ideally, but most of them have bilingual menus. The food is divine, the wine even better and the hospitality usually excellent.
Spanish Steps
The most romantic location in all Rome. Amazing at night. A great location for people watching (a favourite Italian pastime). Below the Spanish Steps you will find Rome's premier shopping district. Unbelievably beautiful shops (and prices!). Do yourself a favour and set aside a couple of hundred bucks to buy your new wife a "surprise wedding gift" here. She will go wild. Just stick to your budget! You can spend anywhere from $50 to $500,000 (I'm not kidding).
Fountains of Berlini
Berlini, perhaps one of Rome's most famous sculptures, has many fountains scattered around the city. If you like classical art and sculpture (as I do) these cannot be missed.
Trevi Fountain
Beautiful to look at, but very very busy. You throw a coin over your shoulder into the fountain and legend has it you will return to Rome one day. It's worth visiting, but try to get there before the crowds.
Panthenon
Originally built as a temple to "All the Gods" by the Romans, this was the world'd largest dome for over a thousand years. Can you imagine the technological and engineering skill required? It's amazing. It has survived because the Christians adopted it as a church. Now it houses the graves of famous and important Italians (kinda like the Panthenon in Paris).
River Tiber
Well worth strolling along, especially as you wander towards the Vatican. Very romantic.
Wow... I'm getting all excited just thinking of it all again. This is all from memory. I hope you have great fun. It will be a honeymoon to remember your whole life.
Mr Mephisto
PS - Rent and watch the classic movie "Roman Holiday" before you go!!
EDIT - I just reread this and my spelling was terrible! Apologies to all...