Well, after a good sleep, a bunch of fruit, and a quick chat to some friends who were online, I was feeling mostly recovered. I decided sitting around in the hotel room wasn't really helping so I wandered across the road to the train station and came in to the centre of town.
Looking over everything is the Fernsehturm TV tower, which you can ascend to get a great view. So I spent a chilled-out hour or two going around that working out where all the various landmarks were.
The other tourists were quite amusing – I helped explain a couple of things to a couple whose nationality I needn't get into. I moved on but while nearby a little later I overheard them having a long argument about whether the information signs corresponded to what was visible out that window, eventually concluding with one convincing the other that they couldn't, as the tower was rotating.
During this 5-minute argument they were standing right where I'd left them 10 mins before… since which time the view had remained exactly the same… because we weren't rotating. And that would be why the picture on the sign looked just like what was on view. Some arguments can be settled by looking out the window!