I live in Naples, rather than Rome, but I will give a few pieces of advice that is more of the blending in and being familiar with your surroundings stuff. KNowing what places to visit, etc is really easy in Rome. Just get a good guide book.
Be prepared for rain. Dec is part of the rainy season. It can be miserable.
Carry a small packet of Kleenex in your purse. You may encounter a bathroom that requires you to pay for paper (they decide how much you will get). Some bathrooms (such as those found in the train stations and airport) require money for entrance. Have Euro change handy. Some bathrooms have attendants. It is not ok to stiff them. Even if you only give 10 or 20 cents, drop something in the plate. You can even encounter attendants in a McDonald's restaurant.
Of course, do the touristy stuff. I highly suggest hitting the Sistene Chapel very early in the morning. The waiting line can be very long and extend around the building. At the Coliseum, enter the Forum. At the entrance of the Forum, in the evenings, there is an old lady who feeds the stray cats. She calls them by name and they really do come running. I am a cat lover, so this was a highlight of one of my day trips. She will have a sign asking for people to donate money so that she can feed the cats. You don't have to give money, but it would be good for the strays.
Street vendors are funny. Of course, you are in Europe, so you can haggle. Go cheap. My husband can get the initial price of 20Euro for a pair of knock off glasses down to 20Euro for 2 pair. If they don't accept what you want to pay, just walk away without speaking. They will chase you down if they want to sell the item. Don't fall for the "You are my special American friend. I give you special price."
To them, ALL Americans are their special friend because most are afraid to haggle and they pay whatever price they are told to pay.
Trevi fountain is most beautiful at night. Beware of the vendors walking around with cheap crap in their hands. They can actually ruin your experience. I swear there are dozens of them and the piazza is not that big. Seems as one leaves you alone, another one is bugging you. Don't accept a rose offered to you. They are being sold. Accepting one means you will pay for it. They like to catch Americans off guard. We generally accept things being handed our way. Have some gelato in the ice cream shop at Trevi fountain. They will let you sample if you ask.
The pizza is very different from American style. I have found Rome to be more geared to tourists than Naples. Just basic tomato sauce and a few chunks of buffalo mozzarella cheese in the center is the traditional Italian pizza from Naples. The taste will be slightly off since that cheese is made in my region, but give it a try. Completely different texture. Rather spongy/rubbery. If you can get past the initial shock of the flavor and texture, you will learn to appreciate how good it is and never want traditional mozzarella again. If you order a pizza, it is meant to feed one person. The crust is thin and there are few toppings. You can grab a slice in small shops. Basically, the pizzas are made ahead of time and they warm the slice on a small grill as you order. Don't be surprised if you see a sliced hotdog and french fries pizza. WARNING WARNING!!!!!!!!!! Don't ask for a pepperoni pizza. Pepperoni is Italian for green bell pepper. So, if you want a green bell pepper pizza, ask for a pepperoni pizza. The closest to American pepperoni you will get is a spiced salami. The pizza diavola would be a good one, but it also has hot pepper juice, etc on it to make it hot. I suggest you get a fried rice ball. Don't ask what the mushy/pasty stuff is in the center. I don't know. All I know is the rice balls are one of my favorites.
Try eating at a trattoria. This is a small family restaurant that is usually attached to someone's home. They are usually found in an alley. You will find few tables and most likely will be able to see the kitchen from your seat. Mom might even be cooking in her nightgown....lol. The menu is limited since they are just cooking one or two things each day. Great food. The good restaurants (non-tourist) will not have salt or pepper on the table. Don't insult the cook by asking for it. Pasta will be al dente (slightly chewy). If you get a touristy place, they will cook it mushy to your liking without having to ask.
watch out for thieves. They are everywhere in Italy. Have wallets in the front pockets. Wear purses with the strap across your chest or if not, always make sure the purse is held with your hand and a bit to the front. Keep wrist straps utilized for all cameras. Watch out for scooters. They like to buzz by for the steal. Subways are famous for thieves. Just be aware of your surroundings. If you find you have been pickpocketed, no need to go running after him. I guarantee he ran out of your car and made the pass to his buddy in the car behind you. A British tourist had this happen on my last trip. Sad that he really thought he was going to get his wallet back. You will likely encounter a belt salesman on the street. For the men, don't allow this salesman to grab your pants waist and shake the pants up and down in an attempt to convince you that you need to buy a belt. What he is most likely doing is distracting you from noticing a hand in your pocket. Easy target and loss of wallet.
Don't give to beggars. Do the locals a favor. They are annoying. We prefer they go back to where they came from or just move on from lack of sympathizers. As a warning, giving to them will only mean they will follow you and ask for more. In addition, if it is a small child of 2-5 years, they might even latch on to your leg like a monkey and not let go until you give them more. It happened to a couple that was on one of our tours.
Don't walk out in front of scooters or Smart cars. They don't stop for anyone. Crossing the street, at least in my area, is a learned skill. if you find yourself having trouble crossing, just find some locals and blend in with them as they cross. They know what they are doing. We had to use this technique for a while until we caught on to the system
I remember one day we went downtown and stood at a corner for a good 15 minutes waiting to cross. A man sitting at that corner walked over to us, grabbed our hand and just walked across as pretty as you please. We just looked at each other with disbelief.
The Euro exchange rate is killing us right now. Be prepared. Oh, and the Italian brand name stuff such as purses, etc are not as cheap as most people like to make you believe they are here in Italy. Just the price tag in the window will make you gasp. Then, add 40% for the exchange rate.
Go find the African selling the knockoff
.
That is all I can think of right now. Enjoy your trip.
They will know. 
Here, the main pasta is penne.
