From the airport
Train: Take the S1 from Hamburg Airport to Barmbek station. Change there to the U3 line and travel to Schlump station. From Schlump, the NH Hamburg Mitte at Schäferkampsallee 49 can be reached on foot in approximately 10 minutes. With a valid HVV ticket, you can use Hamburg’s trains, buses and selected ferries within the applicable fare zones.
Taxi: It's a 20 minute trip and is around €30.