As you head along the road between Falkreath and Markath near the Southwest corner of the map, you'll come across a location with a particularly large bridge next to a waterfall coming off of the nearby impassable peaks. You should also notice a cave marked on your top-of-the-screen navigation bar- this is Reachwater Rock. Carefully climbing up the mountainside from the Northwest end of the bridge will bring you to the top of the waterfall. Here you will find a silver vein, a nice view, and a cave behind the upper waterfall.
The first thing you'll find in Reachwater Rock is a cluster of mushrooms alongside a stream. Grab these, then turn left to head downstream and further into the cave. Here you will see a series of stone bridges reaching up to an ancient Nord puzzle door, by way of a large spire of rock in the middle of a pool that covers the majority of the cave. There is a skeleton floating in the water, which you should investigate. The skeleton hasn't got much, but there's a locked coffer at the bottom of the cave that holds considerable treasure- just beware the flow of the water doesn't drown you by sinking you to the bottom, as there are many parts of the pool that you cannot swim upwards in.
Clambering back onto dry land, make your way around the cave gathering mushrooms until you reach the top of the pillar. Here you can find three things of note- a dead adventurer with an important book, the claw that fits the puzzle door, and a note. The note is a warning- this place was deliberately sealed and forgotten, and the note asks that you let it remain this way- what was sealed inside should remain locked up.
The book the adventurer holds gives you more detail- it is Lost Legends of Skyrim, and it explains the legend of Gauldur and his three sons, who fled at the time of his death and were eventually caught, slain, and entombed most thoroughly. While most of the locations supposedly involved go unnamed, the book does mention Folgunthur, which is near the base of the mountain that holds Solitude, away to the North. This will be your first destination on the lengthy quest that is Forbidden Legend- but since you're here in Reachwater Rock....
Solve the puzzle door with the Emerald Claw, as you are no doubt used to doing by now, and open it. This reveals a hall with several more doors slowly retracting into the floor- and a second puzzle door, which your new Emerald Claw is not the key for. Being as you can't break through nor break the lock, and breaking the code doesn't do you any good, you'll have to give up on busting things and instead set your sights on Solitude, where the next part of this puzzle lies.
