Subway from Hamburg to Hamburg (city)
The city of Hamburg is covered by the HVV network operating U-bahn, S-bahn, bus, train and passenger ferry.
From Altona cruise terminal it's only a 10 minute walk to the S-bahn station Hamburg Koningsstrabe. Take the green S1 line to Jungfernstieg in the city center.
At just 300 meters walk from the HafenCity cruise terminal you can find the U-bahn station Uberseequartier. Take the green U4 line and get off at Jungfernstieg in the city center.
Those rides takes less than 10 minutes and trains run very frequent every 5 minutes. A one-way tickets costs about €2,5 per person. You can find more information here.
TIP: The Hamburg card available here is a great option for cruise passengers on a day trip. Costing only €8.90 this not only allows free travel on all public transport for an entire day, but visitors can also get discounts at popular attractions and restaurants.