Eater of Worlds
The Eater of Worlds can be a very tough boss if you're not prepared. A good strategy for tacking this enemy is to take the time to build a large enclosed arena a few dozen blocks above wherever you plan to summon the boss from. This will keep smaller enemies out and the gap will give you enough of a warning to allow you to avoid most of the boss's attacks. Bring a lot of Shurikens if you don't have any flail weapons yet, because they will be able to deal the most consistent ranged damage.
Floating Islands
Each randomly generated world comes with at least one floating island. These contain a chest with unique loot and are interlaced with gold and silver ore. Finding a floating island can be tough as the altitude depends on the size of the world you created, but building a "sky bridge" can help. On small worlds, building the bridge at about 200 blocks above sea level will put you within sight of an island. Keep an eye out for vines floating in the middle of the sky, because that's the bottom of your island.
Harvesting Fallen Stars
Every night time stars fall from the sky. Collecting ten of these lets you increase your maximum mana. On normal terrain this can take a long time and can be a risky proposition in pitch-darkness. By creating a Sky Bridge (by making a ladder about a hundred or so blocks in the air and then laying down stone or dirt in a straight line) you can create a long stretch of easily-traversable land for the stars to land on. With a speed-increasing item such as Hermes Boots or Necro Armor equipped you can travel the length of your bridge collecting stars relatively uninhibited. Zombies will still spawn on the bridge and you might get the occasional harpy or demon eye, but you won't have to contend with rough terrain, chasms, water or anything that spawns from the corruption.
