Hamburg Airport (HAM) is one of the easier German airports to deal with: compact, only 8 km north of the centre at Fuhlsbüttel, and tied into the city by its own U-Bahn line. It serves over 120 destinations and acts as the main gateway for Germany's biggest port city. The U1 runs from the terminal into the centre in about 25 minutes, which makes hotels near Hamburg Airport a practical base for early business flights.
It's a sensible stay too if you're coming from the suburbs north of the city. Several hotels sit within a short shuttle ride of the terminals.