The Mountains of Mirkwood is Third Age name for vast range of hills in northern part of Mirkwood (S. Taur-nu-Fuin)
Mountains were a series of limestone hills with no peak over 2,000 feet high. The range was bounded on the south by the Men-i-Naugrim (S."Dwarven Road"), to the East by the Fens of the Celduin River, to the North East by the territory of the Lakemen, and to the North West by the North-south running enchanted river. The hills were rounded, with twisting watercourses at their base. A few lakes dotted the region and caves wormed their way into bald hills. This territory was inhabited by few men and rather a few dangerous and unsavory creatures. Fell-beasts, Lesser Giants, Trolls, and countless Giant Spiders inhabited this range. The mysterious river-head of the Gulduin began the turbid and dark waters producing dark and hungry dreams should one be bathed in its flow. These headwaters fronted a small lake and waterfall. Known to few was the tower of Sarn Goriwing (S."Abhorrent Spray's Stone") a hollowed spur of rock in the middle of the falls. Few of the speaking peoples had traveled this region except by keeping to the road and then only with great vigilance and many sharp swords at hand.
Note on naming over the Ages:
At the end of the Second Age, there were Silvan Elves living in the western vales of these hills, though at that time the hills were known as S. Emyn Duir (Dark Mountains). That name referred only to the dense shade of the trees, and not to the Shadow that would pass through the Forest known at that time as Greenwood the Great and eventually lead to its becoming known later on as Mirkwood.
The encroaching Darkness was also cause of the change of name from S. Emyn Duir to S. Emyn-nu-Fuin (Hills under nightshade) but the name is connected to the Elvish name for the Forest - Taur-nu-Fuin (after Dol Guldur was built there), and so is usually translated as "Mountains of Mirkwood".