Best transportation from Hamburg airport to Hotel Alster-Hof

The Ubahn is easy. Get the S1 line from the airpoer. Change after 1 stop at Ohlsdorf to Ui+1 T Stephansplaz. Hotel couple of hundred yaerds.

As Lin C states above, take the S-1 Bahn train one station to the first stop at Ohlsdorf station. Transfer to U-1 U-Bahn Line at the Ohlsdorf station. Ride the U-1 line the rest of the way to the Stephansplatz stop in central Hamburg. Total transit time is about 25 minutes. Your €3.80 S-Bahn ticket bought at the airport ticket machine is valid for the entire journey.

Agreed, take the train. Cheaper, and probably just as easy and fast as a cab. Inside the airport after leaving baggage claim, you are at a long hallway. There are two entrances to the S-bahn--one at the end and one near the grocery store. Simply go down (follow the signs with the green circle with the white S. That is the only train, and you can buy tickets at the machine on the landing between escalators down. One stop, then to the blue U1 towards the Hauptbahnhof (direction Ohlstedt / Großhansdorf) and get off at Stephansplatz. Take the exit toward the Colonnaden, where the elevator is. You come up on the street near the Tipsy Baker cocktail bar (I can recommend, was there last week), diagonally opposite the park. Follow the main street 50 yards or so away from the intersection and there you go! The hotel is easy to spot as the side of it is painted with the name.

SUPER easy, trains run every 10 minutes from the airport, and the whole route takes about 30 minutes. The cab might save you 10 minutes and cost a lot more. And if you plan to explore more on your arrival day, getting a day ticket for the train is the best option anyway.