Despite the 9 Euro price, it is worthwhile going down the caves as this gives you access to the castle ruins from which the view is amazing. The caves are the result of years of mining sandstone for the building material for the castle. (Note that the temperature in the caves is a constant 10 deg C. I wore a short sleeved shirt and just survived as it had been very hot outside. I recommend a jacket or similar.)
There are 5Km of tunnels, all of them quite broad and accessible. The floor is mostly even and there is only one flight of steps - short, broad and not steep. The tour takes about an hour. We were the only English visitors and (not unreasonably) the guide spoke only Dutch. There is a information sheet printed in English available - make sure you get one. You can read it in about 3 minutes but the guide drags all the detail out. The interior of the caves is famous for the wall drawings done from the 18th to the 20th century and WW2 that depict the workings of the mine, local legends and actual history. There is also carvings of a "dinosaur" (or at least what people thought a dinosaur might look like) after some fossils were found in the 19th century.
The main failing of the caves is the lack of any illumination other than the guide's lamp. This means that once the guide has had you crowd around some picture or exhibit, he walks off and blackness descends - you have no choice but to follow him. If you have a torch, take it and make sure your camera has enough battery power for flash photos.
I also noted that nobody "counted us all in and counted us all out." This lack of basic safety is a little ironic as one recent true stories is of two boys who, in 1993, died on hypothermia and thirst having been lost in the utter blackness of the caves for 4 days.
Despite the high entry price, the tour ends with a blatant speel from the guide begging and pressurising for a tip - there are even notices on the wall encouraging you to place some money in his hand. A bonus is free stones from the mine for the children - yes, that's right... free stones...
The guided tour stops at the exit from the caves and you are left to continue a very short distance to the castle. The castle is mainly worth seeing for the view. The last owner of the castle blew it up to save it from the invaders (Napoleon B, IIRC) This magnificent strategy destroyed the only castle on a hill in The Netherlands (but then, how many hills has The Netherlands got?) You can learn all there is to learn about the castle from the free information sheet and the notices in Dutch and English at various points of the ruins and you can do this in about 20 minutes to half an hour at the most.
Moving from the castle, there is a café and toilets on the way out.
If you're in Valkenburg, you are duty bound to make this visit. The castle dominates the town and natural curiosity will take you there. If it's raining the caves are a safe bet.
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