Here is an example of an area I remember visiting as a child and have only vague recollections of it. It is a stunning area in the karst region of Slovenia - the same region where the world famous Postojna caves and Škocjan caves are located, however the Rakov Škocjan park albeit less known to the regular tourist, is still a must see.
After you had a good look at the top of the Small natural bridge turn back towards the car park and about 20m down turn left and continue on a track which will lead you to an open cave. The path continues down it and then ends at a tunnel with slippery rocks on the left and a stream on the right. On the other side there is another cave where you cross the stream over a stone bridge (see featured photo on top). The path then leads you to yet another tunnel, this one much longer than the first but still manageable. That opens up into the larger open cave that is located under the Small natural bridge.