Inside of Hyrule Castle, The Master Sword has double the attack power, and never loses energy, making the castle one of the best places in the game to farm monster parts for equipment upgrades.
There is a cave on the northern side of the castle that leads to the dock area. Progressing upstairs you can find an armory with some of the most powerful weapons in the game. It's a great place to visit if you haven't got the 13 hearts needed to earn the master sword.
And on that note, when entering the lost woods, notice the direction that the embers from your torch are falling off, that tells you which way to go. The wind changes direction sometimes, but as long as it is blowing at your back you'll avoid being consumed by fog.