The Elder Scrolls V: Skyrim Tips

Early Pickaxe
There is a mine located between Riverwood and the Three Guardian Stones (Warrior, Thief, Mage). Walking towards Riverwood from the Guardian Stones will take you to the mining cave where you can find the Pickaxe. It should be marked as a hammer icon on the directional indicator.

Be cautious as there are some bandits hiding inside.