I spent new years 06/07in Rome and to tell you the truth, i would have rather spent it at home. Sorry i wont be too negative or you'l stop reading.
bad things about rome/rome in new years:
- its incredibly expensive eg 8- 10 euro beers as a standard price at most bars.
- not much of a party atmosphere
- not much of a cultural experience
i know it doesn't sound that bad, have you been to rome before? i travelled throughout most of northern italy and found Rome pretty dirt with very rude people. i also found the food in room overpriced (for italian standards) and of very poor quality.
if you are going go, there are lost of cheap hotels/hostels around the main train station (termini) might cost you around 70-90 euro per night for hotel and maybe 30 for hostel. this is a pretty unsafe area with lots of people loitering and lots of gypsies. however i'm assuming they have increased prices for new year period. This area however is not very close to the centre of the city, and will take a 10 minute bus ride to get there. (you can walk, but it'l prob take 30-60 mins- which we werre forced to do to get home). It's prob best if you get a hotel close to the centre of the old town. this will cost more, but it means you'l be able to ignore to dirtyier side of rome. while i was there i stayed at a B&B about 10 mins away from the termini (bad idea, too far away)
There are a few pub crawls in rome which is what we did. there is the colosseum pub crawl and 1 or 2 other. they cost about 30 euro. you start off with drinks outside the colosseum (pretty cool) then they take you to overpriced bars. didn't end up finding out where most of the nightclubs in rome are......
if you want to have fun and are on a budget, id suggest somewhere like budapest, ljubljana, even prague. probably more of a party scene for you, more of a cultural experience and much much much cheaper. if you're intent on spending it in italy maybe try a different city.
hope this doesn't confuse you.

