When we visit Italy, we try to eat pizza and a salad for dinner often to hold down costs, and buy foods (yogurt, rolls, cold cuts, bottled water, and fruit) for making lunch in the hotel room, and eat a meal in a restaurant only every other day, if we can. We travel with camping style cutlery (fork, knife, and spoon), plastic cups (for brushing teeth and drinking), a penknife with corkscrew (if you like wine and ONLY in your checked luggage), hand cleanser, and a roll of paper towels to serve as napkins, placemat, and hand cleanser.
You should be aware that in Italy, it is expected that when you eat in a real restaurant (ristorante or trattoria) that you eat at least a first course (soup or pasta) and a second course (meat and vegetable or salad). Nothing will annoy an Italian restauranteur more than Americans who come in and ONLY eat pasta. Also keep in mind that there is almost always a “pane e coperta” (bread and cover) charge of 1 or 2 euros per person, mineral water is usually bubbly (gassosa) but can be ordered without (senza gas), wine is by the liter (1/4 liter for one person, 1/2 liter for two or 1 liter) for 3 or more). But the tip is minimal if at all, rounded up to the next euro perhaps. (Though some tourist places are used to Americans tipping 15 % and may make it clear that they expect it. Resist the pressure UNLESS you only ate pasta, then you might be more generous with the tip to smooth the ruffled feathers!)
Also, if you drink cappucino any other time than the morning (for breakfast) you will be advertising that you are an American and you may get snickers. Finally, do not order a “latte” unless you want a glass of milk. Starbucks would have you believe that latte is coffee but in Italy you need to say “caffe latte” (coffee milk). “Caffe” will get you an expresso (also called “espresso”.)
I would really encourage you to get a place to stay that is centrally located, otherwise you will waste a lot of time commuting to the sights. Also, beware the pickpockets on any transportation (bus or subway) and beware the gypsies on the street. You won’t even know when you were pickpocketed!. Get an under-the-clothes money belt and use it for ATM and credit cards, passport, plane tickets, and most cash. Keep only mugger money in a knapsack, fanny pack, purse, or wallet. (Otherwise, you will waste an afternoon or day at the US Embassy getting a new passport and at the police station filing a crime report…) Be as careful in Rome as you would be in NYC!
We spent 10 days in Rome from Dec 26th into January in 2000-2001. The weather was quite wet though relatively mild (lightweight sweaters under lined raincoats.) I think it rained every day we were there. (And again when we visited Venice and northern Italy in November 2002). But my family swears by that time of year because there are virtually no lines at the tourist sights–just breeze on in!
If you are in Rome for New Years, don’t be outside at midnight. The custom is to throw glass, pottery, and firecrackers out the window. Woe to the pedestrian who gets clobbered! You won’t believe the debris in the streets the next morning!
How much will you spend on food? Boy, that is hard to say. Rome is not cheap, or maybe because I no longer travel like the student I once was. Expect Italy to be like the US but with far less in the way of fast food and no chain restaurants. We spent about $15 to $25 per person eating in neighborhood (not fancy) restaurants and perhaps $7 per person for rolls, coldcuts, water, yogurt etc for lunch. Pizza depending where you eat it and what you drink might run you $5 to $15 per person. An individual pizza (plate size) cost us $10 to $15 in a restaurant when we were last there. A sweet and coffee for breakfast at a bar would probably be $5 per person. (The famous first McDonalds in Italy is at the base of the Spanish Steps. I went there but couldn’t bring myself to eat there, though my family did!)