Hamburg is a city full of lush green gardens and parks. And full of water. You might consider checking out everything around the city center: our inner city lake called Alster, our big docklandish area called Hafen City (harbour city) or the city beaches across the harbour docks. But there are nice canals, too, which are not so well known and can provide you with water views and local people.
One of my favourite spots just next to a canal is called Ufer Café. You sit in the shade of trees with your wine or your beer, but I’d recommend the wine though, because they are specialised wine sellers there…
Inside is a small area to sit during winter time. The café itself is based in an old house which was used for the light-keepers during the times of gas lighting. The wine list is great and they serve nice food with a focus on regional products. On weekends, there is a very nice breakfast selection available.
It is easily reachable by metro and metro bus (the station Hoheluftbrücke is like 150m away). And if you want to check nice arthouse movies, just cross the street and take a look at the screenings at Holi Kino (which has another interesting story to tell on top of their excellent movie choices).