im a regular Amsterdam veteran, i think last count i had been about 8 times.
the last place i stayed in over New Year was cheap and cheerfull (hostel), although the big nigerian security guard didnt take to kindly when he barged into our room at 4am on new years eve and found about 12 people all laying about in various states of consciousness in a 2 person room.... after about 10 minutes of arguing with him, he gave in as we slipped him 20 Euro and 3 marlbros... ill check when i get home for a name and get back to you.
But at least get somewhere nice and central, and i would advise somewhere between Damrak and Centraal... Museum Plein is a very nice place but its a pain in the butt if you are going to red light/centraal all the time... and Vondel Park is a bit dodgy after hours, i had a hotel on the otherside of Vondel once and walking through it at 3am on my own was quite intimidating.... but in saying that Amsterdam has been one of the safest cities i have ever been in. Leidseplein is also a good location... although we always refer to it as Led Zepplin.
And tips on cafe's, stay away from the seedy dodgy ones as they will just rip you off... go to the cup winners... the best imo is The Grey Area, ran by Americans, the freindliest people in the Damski and it has the best err... *produce*.