Most of the bike shops and many hotels have bikes for rent. They charge around 14,- for one day or 9,- for four hours. Also there are some professional bike rentals in the same price level. A good and cheap alternative would be the StadtRAD Hamburg, the public bike rental system. You have to register and pay 5,- once, this money will then be offset against the rental costs. This will most likely not be necessary as the first 30 minutes are always free off charge and you don´t really need the bike longer than half an hour to drive from one highligt to the next. But if so, costs will be 8 cents per minute and the maximum for one day is 12,-. There are several rental stations all over the city, the StadtRAD Hamburg App shows you where they are located. If you don´t feel like downloading the app you can always just ask someone on the street where the closest station is - almost everyone in Hamburg uses the StadtRAD, so I am sure you will be helped!
Very popular and available 24/7 are the Donkey Republic bikes, you can rent them out with the use of an app, their prices are very attractive. What is more important, with voucher code: MYCITYHAM, you will get 10% discount on your bike rental. This might be one of the best offers you can get in Hamburg!