On the way down from Helgen to Riverwood, you should already be close to, if not at, level 2.  This is enough, if you’re careful, to handle Embershard Mine.  This little nook is located along the edge of the mountains, just a touch East of the road near where you spot the three Standing Stones (Warrior, Mage, and Thief).  While it is a mine, it doesn’t actually have much in the way of mineable ore- instead, this is a good chance to practice your bandit-slaying and gather some loot and gear.  While you’re at it, you can also read a book on smithing and get a little practice as well, with a forge, grindstone, and workbench.

There should be only one or two bandits outside, not really enough to worry you as they’re only semi-competent.  After slaying them, approach the mine- which you can now use as a quick-travel location if you’d rather head on to Riverwood and come back with a little more experience or slightly better gear and spells under your belt.

The front area has a tripwire you’ll want to avoid, and a bit further in are a pair of guards- if you care to wait one of them will fall asleep, but sneaking up and filling one of them full of arrows before engaging the other in melee works perfectly well also.  There’s a little bit to gather here, then a short tunnel to a larger cave with a bridge across it.  Traipsing over to the other side gives you a chance to lower a drawbridge to a third opening in the cave- prepare a ranged attack and wait here, you can snipe at the next few bandits as they cross the bridge.  If you have the basic Frost spell, you can generally kill one and maim another on their way across from this distance, letting you then turn and stand in the doorway- thereby forcing them to face you one bandit at a time.

Once that’s done, loot the bodies and head back down to the bridge.  Crossing the drawbridge will bring you to a short tunnel with a single guard- who holds the key to a cell which you can find a chest in.  Once he’s dead, that accounts for all the bandits, so you can meander around and loot the mine pretty much at will.  Tinker with the forge if you like, grab some abundant gear, and make sure you pick up the skill-boosting book on smithing, since you won’t see another copy of this one for a while unless you immediately start in on side quests once you reach Whiterun Hold.