Erebor or the Lonely Mountain was originally discovered by Thráin I the Old after his exile from Khazad-dûm. His descendant Thrór made it into a great city and citadel. Containing a great hoard, including the Arkenstone, it was captured by the dragon Smaug, who was finally overthrown in the days of Thrór's descendant Thorin Oakenshield.
Climb to the top, then work your way slightly down the west slope to an 8 foot high boulder, and look for a secret door at the top of this boulder. Watch out for relatives of Smaug (rattlesnakes) during warmer months.
The dwarves of old built a trail from the north. You can hike along the old wagon road from the southeast, then pick up the remnants of the trail at the marked waypoint. The trail winds up the north slope, reaching the summit from the northeast. It can be hard to find going back down, so there are two additional waypoints which I recommend.
I have added a clue to solving the puzzle for Osgiliath to this cache.