If you have time to relax while wandering round the Speicherstadt district, I would highly recommend coming to Messmer Momentum. There is a little museum about tea attached to it (free, but all in German), but the highlight is really the gentle and classy tea room. We stopped for some toasted sandwiches for lunch, but primarily to sample a few different cups of the huge tea selection. The menu is so robust, it would be criminal to not try something you've never had before, and at 2,50EUR a cup it's pretty reasonably priced, particularly when you consider that everyone will receive a free box of 3 teabags, which you can choose from the shop at the end. The service is not overly quick, but why would you want to rush good tea?
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