Hamburg

On the water? Get a one-day Hamburg Group Card. This will give you both (assuming you are a couple, if you are a single, then just get the basic card) unlimited transit for the day, along with discounts, if you use even 1 you will be ahead. Metro to Landungsbrucken, take Harbor Ferry 62 (web hadag.de) on an out and back, take Ferry72 and get off at second stop, wander warehouse district, if interested the International Maritime Museum is fascinating, you can also take ferry 61 for a great view in the harbor. The city is beautiful, and you can let your interests guide you to what else you wish to see.
Having just been there, we found RS' suggestions pretty accurate.

Rick's excellent and informative Germany Guidebook has a chapter for Hamburg. For one day. I would spend most of in the Hafencity/Harbor area. First thing in the morning head to the Minitur Wonderland model railway attraction, it's spectacular and the city biggest attraction. To avoid the crowds get their when it opens or when it's about to close (it's open till 10pm on the weekends). Walk around the Hafen area a bit and make your way to the harbor attractions, there are historic boats/U-boat you can explore , and lots of seafood eateries. There is only one harbor boat tour in english which is at 12pm. The tour is a bit industrial, but very fascinating. The maritime museum in excellent but massive and will eat-up a big chunk of your day, for just one day I would skip it unless it's raining.

The Rathouse (city hall) tour. It's one of the nicest old city halls anywhere. There are portraits of all the Bergermeisters through the years. One painting (looked like 1950's or 60's) included a guy who looked dead with his wife, complete with Cruela Deville cigarette holder and scowl. We got a lot of laughs thinking about that painting.

A boat tour of the harbor, it's considered a good tour if it includes the old warehouse district (can't recall the name of the area).

Churches where Martin Luther preached.

Parks and/or beaches (man made on the harbor in summers) on a nice day.

St. Pauli used to be the red light district (think St. Pauli Girl beer), but is now the chic/expensive place to see and be seen.

Walk around the Binnenalster and ask yourself why all cities can't be this attractive.

PS- The St. Pauli district, Reeperbahn included, is still very much a red-light district. There are plenty of clubs of the non-sexual variety, but still countless places where a lonely sailor on shore leave can... well, you know. And no shortage of gambling parlors, "date bars", Thai massage parlors and other sorts of institutions. Although mabye not quite up to its infamous reputation of "the most sinful mile" , St. Pauli is still far from gentrified and remains quite a bit of its raw energy.