Hey there, welcome to Manchester
You should try Laterooms, they are really good for last minute deals
http://www.laterooms.com/en/Hotels.aspx?k=manchester&r=0&n=0&d=20061228&rt=0,0&c=1 I had a look for you and the best deal on there is the Britannia Airport Hotel, it would mean you don't have to cart all of your stuff into town, + it's only £30 per night for a double room, usually £85 per night!
If you are moving to the city for a while, I'd definately recommend getting yourself a Citycard. We use the hubbies a lot and they save you loads of money on eating out, cinemas etc- see
www.citycardmanchester.co.uk.
Enjoy NYE and hope find yourself a nice place asap!
ps, for renting, can recommend an agent called M1, located on Whitworth Street West in the city centre- very good service
http://www.ls-1.co.uk/