As far as short adventures for the setting... the adventures written for the 3.5 release are all good in my opinion. There's the group of four connected adventures -- The Forgotten Forge (found within the Eberron Campaign Setting book), Shadows of the Last War, Whisper of the Vampire's Blade, and Grasp of the Emerald Claw that all form a really nice bunch of adventures that hit many areas of Khorvaire and Xen'drik and show off a lot of what makes the setting cool. The longer Eyes of the Lich Queen adventures is also really nice for showing how the dragons of Eberron interact with the setting, and highlights the southeast corner of Khorvaire (Q'Barra and Llhazaar Principalities) and Argonessen in a way that most other Eberron material does not. Q'barra is cool because Keith Baker uses the area in it called Hope as a location for a "wild west" kind of adventure setting and has talked about what he's do with that on his blog. Q'barra is also the nation recommended for placing Ghosts of Saltmarsh (if you own that book and want to use those adventures within the setting.)