The public transport system, including buses, U & S-Bahns and ferries, is relatively easy to navigate for individuals with disabilities. Most stations have lifts that offer easy access to the platforms for wheelchair-users and other with limited mobility. You can find the list of barrier-free stations here (p. 27). On U & S-Bahn platforms, raised markers direct visually impaired individuals to the doors of the train, and buses carry access ramps to ease boarding for anyone who needs it. On trains, buses and ferries, there are special seating areas dedicated to wheelchair-users and those with special needs, and the upcoming stops are both announced via loudspeaker and displayed in writing.
If you're staying in Hamburg long-term, you might want to request a special pass allowing those with disabilities as well as their companions to travel for free. Here, you'll find a German-language explanation of this pass, called a 'Schwerbehindertenausweis'.
Plenty of Hamburg's museums, landmarks and activities are accessible for those with special needs. In front of the City Hall on Rathausmarkt, a bronze scale-model of Hamburg provides a fun way to gain a first impression of the city, both by touch and by sight. Take a look at this website for a map showing everything from parking spots and public bathroom facilities to the best wheelchair-friendly shopping and sightseeing routes around Hamburg.
The Fischmarkt markets, the Landungsbrücken piers, the Cap San Diego ship, St. Michael's Church, the planetarium, the Planten un Blomen park and Hagenbeck's Zoo are some of the barrier-free highlights the city has to offer. In addition, most museums in Hamburg offer discounts to people with disabilities and their companions, and are barrier-free. This is the case at, for example, Hamburger Kunsthalle, Museum für Kunst und Gewerbe, International Maritime Museum, Miniatur Wunderland, Deichtorhallen, Bucerius Kunst Forum, Hamburg Dungeon and Dialog im Dunkeln.
If you're visiting Hamburg and looking for a place to stay, there are plenty of accommodations that are barrier-free or otherwise suited to your needs. Search for hotels that are wheelchair-friendly and have lifts on this list by Hamburg Tourism.