I've only DM'ed one session in the Feywild so far (...and three in the Shadowfell, which I've made a cross between the expected undead-fest and a post-apocalyptic Fallout-style wasteland at the end-of-time).
The Feywild session was very "fairyland". Social puzzles and tricksy fey. It was loosely based on an old Dungeon magazine adventure. A humble villager accidentally stumbled through a portal to the Feywild and ended up as the "guest" of a band of amused fey (eladrin) who were fulfilling his every dream (food, wine, music) at a feast, while secretly mocking his mortal clumsiness and stupidity all the time.
The PCs were sent to find the villager, running afoul of various encounters: an evil fey (ettercap) and his spider minions, prankster sprites, woodland paths that shift and change, a riddling gnome, an arrogant eladrin knight on a fey steed who challenged the mortals to a duel, and finally a skill challenge to convince the feasting eladrin to let the villager go back to the mortal realm.