Rivendell, city of elves and home of Elrond, was founded in year 1267 of the Second Age. Located at the foot of the Misty Mountains, and in the steep valey Imladris, it was built in the "wedge" of land between the Hoarwell and the Loudwater (Bruinen). The magical waters that surrounded the valley were said to be under the power of Elrond, and they would rise up at his bidding to keep out any attackers.
                             ______________________________|||||||
                       _____/ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~|||||||
                      //~~~~~/                             |||M|||
                     //                                    |||I|||
    	           //     ;;                              ///S///
    	          //     ;;;;;;                          |||T|||
   	        N//      ;;;;;;;;                        |||Y|||
   	       E//      ;;;;;;;;;;                      ///////
               N||      ;Rivendell;                     |||M|||
East-West     I//      ;;;;;;;;;;;;                     |||O|||
  Road       U//_________,__________________________    |||U|||
.           R//~~~~~~~~~,~~~~~~~~~~~~~~~~~~~~~~~~~~\\  ///N///
 `..       B///        .`    RIVER HOARWELL         \\ |||T|||
    `.     ///       ,`                              \\|||A|||
      `;..%%%.......`                                 \///I///  
         ///    FORD                                  ///N///
        ///                                          ///S///
       ///                                          ///////

(My ASCII art needs work, but you get the idea)

Rivendell became known as the Last Homely House East of the Sea, eventually serving as a refuge for Bilbo on his quest to Erebor, and nursing the Company of the Ring near the end of the Third Age. Even the Dunédain often visited there. (Indeed, Aragorn son of Arathorn was raised by Elrond himself; it was in the woods surrounding Rivendell that Elessar first beheld Arwen Evenstar - see The Arwen/Aragorn Issue.)

Imladris was an immortal land, holding an untarnished and beautiful magic. Little was it known that one of the Three Rings was hidden there. This was Vilya, "Ring of Air" - it was given to Elrond by Gil-Galad before he died. When the One Ring was destroyed, the power of this ring faded - and so did the "magic" of Rivendell. Soon after the fall of Sauron, Elrond departed for the Grey Havens and left Middle-Earth forever. The remaning Elves soon followed, and the valley of Imladris was eventually deserted.

J.R.R. Tolkien Node