Being surprised at is usually a more measured reaction than being surprised by something - which is a more instantaneous reaction.
During his two-month tour, he was often surprised at his hosts' generosity.
While sitting watching the TV, he was surprised by the door-bell - who could it be at this time of night?
There's also a figurative meaning of 'surprised at' (struck by something's moral unexpectedness): a teacher at my primary school once said, memorably 'Robert Knowles, I'm surprised at you' (she was quite easily shocked, but the word I'd used was rather shocking ).
Owls hunt by night.