Empire Riverside Hotel

you can get there by U3/S1/S3: Landungsbrücken, and then walk along the river elbe. In 5 minutes you will reach the tall building. You can walk to St. Michaelis and the Port in 5 minutes and to the historical museum in 10 minutes.

Directions: really riverside, near Landungsbrücken 6
best views over the city and the river elbe, but near the famous red light district and the Erotic Art Museum (Bernhard-Nocht-Strasse 69).

There are some design hotels in Hamburg in case you are interested in that. Of course prices definately are no budget option! But still - I cannot imagine to spend that much but be happy if you can afford...
So these are the names and websites of the most known Design Hotels (of course I did not check the quality myself...)

Empire Riverside
This is the latest opened design hotel in Hamburg. Designed by architect David Chipperfild who took inspirations from the modern architecture in the 30s and from the ocean liners of that time. All the rooms have windows with a view on the harbour. Prizes start at around 150 €. Very cool is also the cocktail bar on level 20 where you have the greatest view on the city and harbour. It opens at six in the evening, and it is definately recommended to book a table around one week before. But you also might check if something is free. It is situated by the harbour, close to Reeperbahn and St. Pauli - so very central.
www.empire-riverside.de

SIDE
5 star luxury hotel, central location, architects Jan Störmer from Hamburg, Interior made by Matteo Thun, Lighting concept by Robert Wilson. Starting with around 200 EUR for a double room.
www.side-hamburg.de

East
Fusion of nightlife, gourmet and design, St. Pauli area close to Reeperbahn, designed by Jordan Mozer, former industrial building from brick stone. Starting with 180 EUR for a double room.
If you cannot afford a night but you still want to get a glimpse inside: my friends says they have supergood cocktails...
www.east-hamburg.de

Gastwerk
This also is an hotel in a historic industrial builing, rooms with loft atmosphere. It's not that central but still OK. Close to Altona/Ottensen which is a hip area to go out. Starting with about 135 EUR.
www.gasterk-hotel.de

25hours Hotel Hamburg
Belongs to the Gastwerk Hotel somehow but it's younger, fresher, more modern designed - still in the retro-look from the 60s and 70s. Starting with 100 EUR.
www.25hours-hotel.de