Before you leave Helgen you should find at least one 2 hand battleaxe or hammer. Yeah, they're "only" iron, but they do way better damage than 1hd weapons. In Bleak Falls, I think you might find a least one 2hd enchanted weapon.
Falkas drops a Skyforge Steel 2 handed sword, when he turns into a werewolf. This is pretty early in game and surely is one of the best 2handed weapons you can find in game as you upgrade & enchant it.
My 2nd char took a battleaxe out of Helgen. Which is what I wanted anyway. Though I later upgraded to skyforge steel. In Bleakfalls Barrows, the Draegur have all sorts of 2h swords. Their's a cave not to far out of Whiterun that usually has a hammer or two.
Spoiler
go strait past honeybrew meadery up the mt road 1st cave on te right. Bandit hideout. I usually do that cave before lvl 12. Sometimes the whiterun guards mention it.