Stay at Meridien or Kempinski
Try to stay in the Meridien or the Kempinski at the Binnenalster. Both are just a few meters from each other, but people prefer either one of the two and you'll have to try what you like better. Kempinski is more of the old traditional hotel, while at the Meridien everything is modern. All rooms at the Meridien seem to have large flat-screen TVs, not that you get a chance to use them very often when you visit the city. The brkfst at the Meridien is excellent and the view from the top floor is just incredible in the morning. Brkfst at the Kempinski is equally nice - they just didn't have any Nutella - but the view is not as nice :)
Don't stay at the Radisson at central station if you can help it. It is a good hotel, but it's too loud and the bkfst is just ok. - Although if the other two Hotels are booked, you might want to give the Radisson a fair chance! :)
Madison
Madison near Hamburg harbour is great to stay at. Nice restaurant within the same building and just a few minutes to harbour. Really good suite services available.
Hotel Wagner
If you don't want to spend all your money for just one night, this is the a good tip: Stay at Hotel Wagner. It's beautiful located in Hamburg-Rotherbaum close to the ICE railway station Hamburg-Dammtor and the University of Hamburg and with bus connections to Hamburg central station and other tourist destinations in a few minutes.
I stayed there for one week while I was doing an internship in Hamburg near by. The staff is really helpful and it has free wifi, too! That's one of the points a good hotel need in my opinion so that you can do stuff and finish work from hotel, too.
The style is also amusing: Hotel Wagner tries to catch old Hamburg style and combines it with new elements, really cool!
The building where it is located is called Dammtorpalais which houses five hotels. Although in a very busy, but also safe, district of Hamburg, the Hotel Wagner is still very noiseless (if you don't get one of the rooms at the beginning of the floor wich everybody is passing to go to their own rooms).
Madison Hotel Hamburg
My hotel tip for Hamburg, very pleasant, comfortable, cosy, upper class hotel, look for special arrangements for your stay. Central location in a very nice area of Hamburg.