As usual in the German north sea tourist locations the harbor has fish restaurants everywhere and not much else. In my experience these places rarely have vegetarian or much less vegan options at all and even if they did most veggies probably wouldn't want to eat there because of the heavy dead fish stench.
This is a small place with traditional Italian ice cream and I was glad to find out that they have some vegan fruit sorbets beside the regular dairy sorts as well. When I visited it was 6 options of various fruits which should be enough to try for two or three visits on a holiday, I think. I tasted all 6 sorts on my one week vacation and they were all very tasty. The atmosphere is nothing special, but at least you can sit outside. The tourist shop next door has a toy firing squad car that was a nice distraction to out little boy so my wife and I could enjoy our sorbet in a little peace and quiet, maybe that is interesting for someone else too.
Cons: regular dairy ice cream