Valkyries

The Valkyries were female virgin warriors who armed with helmets and spears rode upon horses. It was their decision who fell in battle, there would be six to thirteen Valkyries present at any single moment. They would take half  the selected dead to Valhalla whilst the other half would go to Freya's afterlife in Folkvangr. Freya would choose the half she wished from the fallen Vikings. Odin would grant the Valkyries permission to enter Midgard in the form of a white swan, but should they be seen out of that form they would become mortal and would never be able to return to Valhalla. The most famous of the Valkyries was Brynhildr whose name means Bright Battle.

(Image Source; http://www.viking-mythology.com/)

Nidavellir

The home of the Dwarves, the Dwarves were a race that lived in caves and underground. The King of the Dwarves was Hreidmar. They were known throughout the nine realms as masters of craftsmanship, with many of the Aesir receiving gifts from them. Thor's hammer Mjolnir was a gift along with Odin's spear Gungnir.

(Image source; http://www.goddessfreya.info/myths/nidavellir.htm)

Svartalfheim

The home of the Dark Elves. The dark elves detested the sun and as such lived in beneath the ground; they were hideous creatures who caused many problems for the humans of Midgard. The dark elves were known to cause trouble throughout the nine realms; causing nightmares in many of the inhabitants. In Norse Mythology dark elves were also known as Mare, they would rest upon the chest of a sleeping person and whisper nightmares into their ear in order to haunt their dreams.It was also believed that if a dark elf was touched by sunlight they would immediately turn into stones.

(Image Source; http://www.fanpop.com/clubs/norse-mythology/images/23500281/title/svartalfheim-photo)

Jotunheim

The land of the Frost Giants or Jotunn. The Jotnar were the sworn enemies of the Aesir and were constantly at war with one another, however there were Jotnar who had love affairs with the Aesir, Thor and Odin both had a few Jotunn lovers according to mythology. Loki was in fact a Jotunn himself but was accepted into  Asgard as Odin's son and Thor's brother  (I should point out that in the sagas it has never been confirmed if Loki was adopted by Odin or simply included in the royal family as an extra.) Jotunheim was separated from Asgard by the river Iving which despite Jotunheim's sub-zero temperatures never froze over.

Jotunheim was believed to be a frozen tundra, consisting of rocks and dense forests. The Jotunns were forced to hunt animals from the forests and fish from the rivers due to the infertile land of Jotunheim. The world itself was believed to have been created from the Giant Ymir's head, who was as previously mentioned killed by Odin and his brothers.

(Image sourced; http://norse-mythology.org/cosmology/the-nine-worlds/jotunheim/)

Midgard

Midgard-The 'Middle-Earth'. Connected to Asgard by the Bifrost, Midgard is the home of humans. Surrounded by a vast impassible ocean and it was in this ocean that the Midgard Serpent (Jormungandr) resided. The Midgardians (humans) were granted permission by Odin and his brothers Vili and Ve to live on Midgard after the creation of the first humans.

(Image sourced; http://elderscrolls.wikia.com/wiki/Whiterun_(Skyrim))

(The image is Whiterun from Skyrim, it was the best representation I could think of)

Alfheim

Alfheim- The home of the Light Elves.  Alfheim sat beside Asgard on the upper level of Yggdrasil. The light elves were beautiful creatures, considered the 'guardian angels' of the ancient Nordic world. They were minor gods in charge of nature and fertility who would influence humans with their magic. They were often considered the inspiration for all art and/or music.

(Image sourced; http://the-kundalini.com/alfheim-elfs-home-norse-myth/)

Vanaheim

Vanaheim- The home of the Vanir. The Vanir were ancient gods who were masters of sorcery and magic, throughout Norse mythology they are known for their ability to predict the future. No one knows of the exact location of Vanaheim or even what it looks like. There was a war between the Aesir and Vanir for many years but at the end of the war three Vanir went to Asgard; Njord and his children Freya and Freyr.

(As Vanaheim is the unknown realm there is no depiction of it, however many believed it to look similar to Alfheim)