So for a harbour trip if you don't speak German (though I am guessing you do), Maritim Circle Line. It's a HOHO, so plan accordingly if you want to visit any of the stops. Otherwise for the German language ones simply ask where they go. The bigger the ship, the less they go into the canals. Or you can simply use your HVV or Deutschlandticket to ride the ferries around the harbour. No commentary or up close to the big ships, but hard to beat the price if you just want to see HH from the water.
For MW, I would budget a minimum of 3 hours. Depending on your level of interest and stamina, one could easily spend days and days. I find 3 hours and I am at my limit, but everyone is different. We are going on Thursday, and I haven't been in 2 years. My husband has somehow never been. We are going for the last 3 hours before closing, so hopefully it won't be as crowded, but we are automatically time limited. I can report back then.
As for what else you should do that is quintessentially Hamburg, the answer is obviously a musical. If you speak German, definitely try for Heiße Ecke--a musical about the Reeperbahn that has been running for many years. It has something like 70 characters played by 9 actors--really fun even if you don't speak much German, and super funny if you do. Or go with something like The Lion King if you want more traditional.
And of course the things to see in HH include sites like the Elphi (free to visit the observation deck and a very short ferry ride or walk from Landungsbrücken / harbor tours / MinWun), the Michel (visit the Krameramtstuben just behind it), the Nikolaikirche ruin / memorial (both churches easily walkable from Landungsbrücken and your hotel), the Alster (probably won't rent a boat in February, but you still need to at least see it, even if just a quick stop at Jungfernstieg/Rathaus) and if you have tons of time, the Treppenviertel and beach in Blankenese. Those are the things that I would recommend to most people, including those who live in Germany.
Also near where you are staying (between the Nikolai and the back of the Rathaus) are the Trostbrücke and Pudelhaus, the Altes Rathaus, and the Deichstraße. Be sure to pop into the alley between the houses, down to the water, and look at them from the Fleet.