The problem is the 'prediction loop', which has no clearly defined exit. There's no path that can be followed that will terminate it:
The demon understands every part of your brain, and knows that if it says that you're going to watch TV while you're determined to prove it wrong will make you listen to the radio instead. So it enters the next iteration of the loop. This cycle would continue for infinity, which is where we perceive a paradox.
There are several naive resolutions that come to my mind. Assuming that predicting the future takes some time, even if it's only a fraction of a second, will allow a way out. The Demon will simply enter the loop and exit it once the evening has passed and every possibility of 'predicting it' has vanished. Of course this could be considered cheating, it has never been established if the Demon's computations take time or not, but asking this question can be considered cheating as well, since it's probably impossible to have _only_ two possible things you could be doing. Which introduces the second solution.
The Demon is more intelligent than you are, and while you'd sworn to yourself that there were only two possible outcomes to this evening: doing the opposite of what the Demon predicts, the Demon sees beyond the 'two' possibilities and correctly predicts a third possibility that you didn't envision.
The last solution attacks the notion of free will, if the Demon can exactly predict the future than this implies that the universe is deterministic. So instead of having only two options, or a third invisible option, there is only one real option and the demon cannot be wrong or it cannot be right.
All of these 'solutions' either introduce a new or alter a previous assumption and are thus not really solutions to the question asked, as it stands I think the question is unanswerable and introducing new concepts and ideas is inevitable.