I don't know what level your character is but if you're 14 or so, you should safely and relatively easily be able to make the loop of Westfall that I did when starting out as a miner. Hop the tram to Stormwind then head southwest along the mountains to the Westfall bridge. Cross and start making the loop by heading north and then west. You'll hit the Jangolode Mine and then the Gold Coast Quarry. Copper, Tin and Silver (much less) pretty common and sometimes respawn while you're still in the mine. Copper pops up all along the route so stick close to the mountains. A little bit later at maybe level 18 or so, start including the Deadmines and maybe even the instance if you can get some help from non-miners. At high level, you should be able to pick up 40-60 Copper and 20-30 Tin in about an hour or so. Silver is a bonus along with the occasional gem.