Mining 1-300 - Vanilla

1-66: Copper
Horde - Durotar , Alliance - Elwyenn Forest (Go see your Mining Trainer at 66)

66-125: Tin and Silver
Horde - The southern barrens , Alliance - The Weltands (Go see your Mining Trainer at 125)

125-175: Iron and Gold
Horde/Ally - There are multiple places - Desolace, Ashenvale, The Badlands, Arathi Highlands, Stranglethorn Vale. Razorfen Kraul
(Go to your trainer at 175)

175 - 251: Mithril and Truesilver 
(Go to your trainer at 225)
Horde/Ally - There are multiple places - Blasted Lands, Searing Gorge, The Hinterlands, Western Plaguelands, Aszhara, Felwood, Winterspring

251-300: Thorium 
Horde/Ally - There are multiple places - Un'goro crater, Azshara, Winterspring, Eastern Plaguelands 

Alliance
Loch Modan (Thelsamar) - Brock Stoneseeker
Dun Morogh (Gol'Bolar Guarry) - Dank Drizzlecut
Stormwind (The Dwarven Ditrict) - Gelman Stonehand
Ironforge (The Great Forge) - Geofram Boldertoe
Darkshore (Auberdine) - Kurdram Stonehammer
Duskwood (Darkshire) - Matt Johnson
Dun Morogh (Kharanos) - Yarr Hammerstone

Horde
Thunder Bluff (Lower Rise) - Brek Stonehoof
Undercity (The War Quarter) - Brom Killian
Silverpine Forest (The Sepulcher) - Johan Focht
Durotar (Razor Hill) - Krunn
Orgrimmar (Valley of Honor) - Makaru