A list of all the zones where you can get the materials easily for Herbalism and Mining sorted alphabetically by Zones. They are screenshots of my maps in-game from the 4.3.4 Gathermate. All of them up-to-date till November2013.

Eastern Kingdoms:

Arathi Highlands:

Herbalism -
Bruiseweed,
Wild Steelbloom,
Kingsblood,
Grave Moss,
Liferoot,
Fadeleaf,
Khadgar's Whisker,
Stranglekelp,
Goldthorn.

This place is teeming with herbs all around the edges, you'll fill your bags long before you finish a single round.

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{These might not seem like a lot of herbs, but there were so many, I just couldn't get myself to collect all of them so they're not recorded.}

Mining -
Tin,
Silver,
Iron,
Gold,
Mithril,
Truesilver,
Lesser Bloodstone.

Badlands:

Herbalism -
Dragon's Teeth,
Firebloom,
Sungrass,
Golden Sansam.

You can find a lot of Sungrass, Dragon's Teeth here.

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Mining -
Gold,
Mithril,
Iron,
Truesilver.

Mithril, all around the place. Some Truesilver around the south-west, near New Kargath and one or two Gold, Iron veins.

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Blasted Lands:

Herbalism -
Gromsblood,
Golden Sansam,
Dreamfoil,
Mountain Silversage.

You can find the high level Vanilla materials here. Dreamfoil, Mountain Silversage, Grom's Blood.

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Mining -
Small Thorium,
Truesilver,
Rich Thorium.

Burning Steppes:

Herbalism -
Firebloom,
Sungrass,
Dreamfoil.

Mining -
Gold,
Mithril,
Truesilver.

You can farm Truesilver, Mithril, some Gold and Thorium here. Dreadmaul Rock in the east is the best place to farm Thorium.

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Elwynn Forest:

Herbalism -
Silverleaf,
Peacebloom,
Earthroot.

This isn't the best place to farm herbs for Alliance, the best place is Loch Modan, but you can find herbs if you fly around the hills on the northern side of EF.

Mining -
Copper.
Silver,
Tin.

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Hillsbrad Foothills:

Herbalism -
Mageroyal,
Briarthorn,
Bruiseweed,
Grave Moss,
Liferoot,
Stranglekelp.

More herbs than Arathi Highlands here. Liferoot along the river or the lake, Fadeleaf around Sludgeguard Tower in the middle. Some Briarthorn, Bruiseweed Wild Steelbloom and Mageroyal along the western side and in the Uplands.

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Mining -
Tin,
Silver,
Iron,
Gold.

Westfall:

Herbalism -
Silverleaf,
Peacebloom,
Earthroot,
Mageroyal,
Briarthorn,
Bruiseweed,
Stranglekelp.

Mining -
Copper.
Silver,
Tin.

This is by far the best spot to farm Copper, Tin, Silver for Horde or Alliance. Plenty of nodes and an insane respawn time, especially the southern edge of the map, near Deadmines.

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Wetlands:

Herbalism -
Mageroyal,
Briarthorn,
Bruiseweed,
Liferoot,
Wild Steelbloom,
Kingsblood,
Grave Moss,
Stranglekelp.

There are a lot of herbs between Greenwarden's Grove and Dun Modr.

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Mining -
Copper.
Silver,
Tin
Iron.

Kalimdor:

Durotar:

Herbalism -
Silverleaf,
Peacebloom,
Earthroot.

You can farm the early mats Silverleaf, Peacebloom, Earthroot in any level 1-10 zones. I found these convenient near Orgrimmar.

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Mining -
Copper.

Copper is easy to get in these areas. Again, you can do this in any starting zone.

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Outland:

Hellfire Peninsula:

Herbalism -
Felweed,
Mountain Silversage,
Dreamfoil,
Golden Sansam,
Dreaming Glory,
Nightmare Vine.

Felweed, Mountain Silversage, Dreamfoil, Golden Sansam, Dreaming Glory around the southwestern border.

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Mining -
Fel Iron.

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Shadowmoon Valley:

Herbalism -
Felweed,
Nightmare Vines,
Dreaming Glory.

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Mining -
Fel Iron,
Adamantite,
Rich Adamantite,
Khorium.

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Terokkar Forest:

Herbalism -
Felweed,
Terocone,
Dreaming Glory,
Mana Thistle.

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Mining -
Fel Iron,
Adamantite,
Rich Adamantite,
Khorium.

Best place to farm Outland mats. Look at the spot just above Aldor Rise in Shattrath for most of the Adamantite Veins.

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Zangarmarsh:

Herbalism -
Blindweed,
Ghost Mushroom,
Golden Sansam,
Dreamfoil,
Felweed,
Dreaming Glory,
Ragveil,
Flame Cap.

Mining -
Fel Iron,
Adamantite,
Khorium.

Plenty of Adamantite, Fel Iron and one or two Khorium Veins along the southern boundary.

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Northrend:

Borean Tundra:

Herbalism -
Goldclover,
Tiger Lily,
Firethorn.

Mining -
Cobalt,
Rich Cobalt.

Very convenient placement of the veins, you can find them all along the east coast. Start collecting just north of Farshire/Valiance Keep.

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Icecrown:

Herbalism -
Lichbloom,
Icethorn.

Plenty of Icethron, Lichbloom along the Glacier.

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Mining -
Saronite,
Rich Saronite,
Titanium.

Saronite, Rich Saronite and Titanium Veins are all in the same spots and there are plenty of them.

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Sholazar Basin:

Herbalism -
Tiger's Lily,
Goldclover,
Adder's Tongue.

Mining -
Saronite,
Rich Saronite,
Titanium.

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Cataclysm:

Deepholm:

Herbalism -
Heartblossom,
Cinderbloom.

You can farm Heartblossom in the inner circle, Cinderbloom in the higher ring.

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Mining -
Obsidium,
Rich Obsidium,
Elementium,
Rich Elementium.

There are a few Rich Obsidium Veins all around Deepholm and some Elementium Veins along the southern border.

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Mount Hyjal:

Herbalism -
Cinderbloom,
Stormvine,
Azshara's Veil.

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Mining -
Obsidium Veins.

Lots of them. Start from Nordrassil and make your way down the mountain along its edges.

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Tol Barad Peninsula:

Herbalism:
Cinderbloom,
Azshara's Veil.

Mining -
Elementium,
Rich Elementium,
Pyrite,
Rich Pyrite.

Best place to farm Pyrite Ore. There are plenty of Rich Pyrium Veins here which respawn very fast and you get upwards of 10 Ore per vein.

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Tol Barad:

Herbalism -
Cinderbloom,
Whiptail.

A good place to farm Whiptail is the swamp just outside of Baradin Hold.

Mining -
Elementium,
Rich Elementium,
Pyrite,
Rich Pyrite.

Twilight Highlands:

Herbalism -
Cinderbloom,
Twilight Jasmine.

The only place to farm Twilight Jasmine. Some Cinderbloom.

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Mining -
Elementium,
Rich Elementiium,
Pyrite.

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You don't have to farm along the river, which is the most popular spot and someone else will always be farming there. You can follow the north route or go north-south from Victor's Point to Crushblow to Obsidium Forest.

Uldum:

Herbalism -
Cinderbloom,
Whiptail.

The most popular zone for farming Whiptail.

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Mining -
Elementium,
Rich Elementiium,
Pyrite.

A few Elementium and Pyrium Veins all along the northern border.

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Hope you find these useful. I know these won't be the only places where you can farm mats. I focus mostly on Eastern Kingdoms. You can add your own screenshots if you want, help the community a bit. :)