Even with what people have said here I was still surprised to see how small the cathedral actually was. The restoration work on the outside seems to be coming to an end from what I gather, there was only scaffolding on the rear, and the majority of the cathedral seems to be in a reasonably good state. The interior of the cathedral was particularly gloomy but I liked this it added more atmosphere to the surroundings. The octagonal chamber was the highlight for me, an architectural oddity and decorated with fantastic tile work, this stands as one of the finest chapels I have been into. I guess this is what the great Byzantine works feel like (though I have yet to visit any of note myself). The fine stained glass windows in the gothic addition helped illuminate the large gold coffin of Charlemagne.
I really liked the architecture of the cathedral it is a real hodgepodge of styles as it was stared in 794 and seemingly added too consistently for the next 1,200 years, the best place to view this is from the Rathaus square (view in the picture).
Unfortunately a massive hangover (damn those Belgian trappists!) and an inability to find the correct door meant I missed the Treasury, and I think this would have really completed the experience. The city of Aachen was quite small and had only a few other things of note, so I think a few hours to see the Cathedral is about enough.
It is about 1 hour from Cologne and is very close to the Dutch and Belgian borders so very well connected. Well worth the trip! I would like to go back at some stage when I am in a better, non post-alcohol state!