As Alliance, the earliest dungeon that you will have access to is the Deadmines. You should wait until about Level 16 to start this, meaning you will need to quest to level until then. If you are doing a spell cleave group however, you may want to wait until Level 20 since that is...
Mining 50-100 – Tin and Silver Horde and Alliance Hillsbrad Foothills– This zone, which was combined with Alterac Mountains in Cataclysm, now has one of the densest areas of Tin Ore ever noted on any map. By staying in the red zone and going in the caves there are a very large supp...