My favorite event will have to go to Pumpkin Moon/Frost Moon, if I have to choose one of the two, Pumpkin Moon all the way, since it's pretty easy (except for the bullet hell of the last wave) and pretty effective money grinder with all the drops. I have a particular grudge towards the Ice Queen of the Frost Moon as she kept on refusing to give me the Blizzard Staff and Snowman Cannon until recently.
My favorite boss? Hmm... the Destroyer is one interesting boss, Plantera is quite fun, Duke Fishron... yeah, him. That Duke, a combination of your dodging skills, quick-thinking, and the ability to use the correct weapons in combat.
Favorite enemy... now that's an interesting question, I have never really paid attention to what I kill... well, I guess the Mimic. It's drops is pretty useful.
My favorite NPC goes to the Guide! Yes, I'm serious. Indeed, he's now useless since I already understand the basics, but poor Guide just get sacrificed so often that I felt bad and tried to build nice home for him (which ended up as an amalgamation of stone boxes).
Favorite Weapon? Flairon or the Terra Blade, I have been using them both ever since I got them. Never left my first and second hotbar, but who knows what will happen when the pillars rises...
My favorite biome so far is the underground hallow, mainly since I like raging trying to get the Rod of Discord (sadly, no RoD yet)