What do you intend to do with the footage you're going to shoot?
If you're just going to look at the video yourself, for instance to review your lesson, you would most likely want to use the position you already found: near the dome light. This, in theory, should capture both the instrument panel and the picture outside. However, in practice, the contrast between those two is so high that no action-cam type camera will ever be able to deal with that. So either the panel will be underexposed or the outside world will be overexposed. The only way around that (additional lighting directed at the panel) is completely unfeasible. So you're going to have to choose what's more important to you.
If you're going to make your video available for public consumption somehow, then please, please, please don't limit yourself to just one mounting position. Even just 30 seconds of video shot from a single viewpoint is extremely boring. In order to make your edited video even remotely interesting it's got to be a mix of at least four different viewpoints. Obviously some of these will be from within the cockpit (forward, backwards, in your face, sideways, passenger view, whatever) but the best videos also incorporate outside views (however check the practicality, safety, security and legality of attaching stuff to the outside of the aircraft) and possibly even footage of your aircraft taken from the ground or from another aircraft.