Rauros:

The Falls of Rauros are in the North-West of Gondor. Located on the Anduin River, the Falls of Rauros are preceded by the Argonath, the Gates of the Kings. The Company of the Ring sent Boromir's body over the Falls as they did not have the time to do anything else such as bury him.

Rohan:

Also known as the Mark and the Riddermark, Rohan was formerly a part of Gondor, known as the plains of Calhenardon. It was ceded to Eorl by Cirion, then the Steward of Gondor. The Men of Rohan are famed horsemen and their horses are justly famous too. At the time of the War of the Ring, Rohan was beset on the West as well as on the East. For on the West was Saruman, and to the East, their allies, Gondor was fighting the Hosts of Sauron. They were victorious in the west, and arrived in time to make a difference in the Battle of the Pelennor Fields.
The capital of Rohan was Edoras, where Meduseld, the Kings' hall stood.
There were several strongholds within Rohan, including Dunharrow and the Hornburg.

The Riddermark:

Another name for Rohan.

Rivendell:

Known as Imladris and the Last Homely House, Rivendell was the home of Elrond Halfelven. Rivendell was founded in the Second Age of the Sun and lasted until some time in the Fourth Age, though Elrond sailed into the West at the end of the Third Age. Most of the Chieftains of the Dunedain, were fostered there, as was Aragorn in his youth. It was located on the Bruinen.

Bilbo, during the Quest of Erebor spent some time in Rivendell, and later left the Shire to live there after his eleventy-first birthday. Frodo stopped in Rivendell for a time on both the trip to Mordor, and his return to the Shire.

Bilbo described Rivendell as "His house was perfect whether you liked food, or sleep, or work, or story-telling, or singing, or just sitting and thinking best, or a pleasant mixture of them all. Evil things did not come into that valley." (H.58)
Sam is recorded as saying: "Well, Mister Frodo, we've been far and seen a deal, and yet I don't think we've found a better place than this. There's something of the Shire and the Golden Wood and Gondor and kings' houses and inns and mountains all mixed." (LOTR.1023)

Rhudar

One of the three regions that Arnor was divided into in the year 861 of the Third Age at the death of King Eärendur. The other two regions were Arthedain and Cardolan. The kingdom of Rhudar included the land between the Ettenmoors and the Weather Hills. South, it extended to the Misty Mountains.

Rhudar had few folk of Dúnedain descent, the majority of those living in the country were Hill-men, who, it was later discovered were in league with the forces of Angmar, lead by the Witch-King. They were in complete control of the country by the year 1375 of the Third Age.

Between 1375 and 1975 of the Third Age, when Rhudar finally fell with the defeat of the Witch-King, they fought against the Dunedain of Arthedain and Cardolan. However, Cardolan fell within a few decades, in the year 1409.

The Hobbit
The Lord of the Rings
The Silmarillion
The Complete Guide to Middle-Earth by Robert Foster
The Unfinished Tales