my best advice - if you can, extend your stay, we did 2 weeks and I wish we could have stayed at least another 3/4 days. Rome is easily walkable once you get to the downtown/colisum/trevi ftn area.
Wander away from the touristy areas, just a block or two - you'll save $ on food/suvineers etc and really get a good feel for the area - don't be afraid to "get lost" a bit in Rome, it's very easy to find a cab and with that handy dandy little business card in your pocket really easy to get back to your hotel.
Learn a few basic frases in Italian (ciao (pronounced chow) is hello and goodbye) and that's all I remember from 6 yrs ago (oh and banka/ATM lol)
the buses/trains are good affordable/reliable transportation but be aware that you will be known as a tourist and keep your hand on your valuables, pick pockets are known to watch/wait for the unsuspecting tourist to slip up (I'm female so kept money tucked here and there so it was not all in 1 place, bra's are great wallets for a littel cash).
Vatacin - I was on a tour so we went really early and was let in before the "public" but I've heard that later afternoons are a great time to visit, less crowded, less lines etc...
Don't be afraid to ask the hotel desk staff for directions/help/advice/recomm's etc - a friendly smile goes a long way.
I don't remember much but if you let us know what cities you'll be seeing I might have some tidbits (Venice, Pompeii, Toramina?).
LUCKY YOU - WISH I WAS GOING BACK!