If you want to run an Eberron campaign in 5E, you will want the Wayfinder's Guide to Eberron. It provides some quick overviews for players and mechanics for player characters.
Once part of the western frontier of the kingdom of Breland, Graywall now lies 50 miles outside the Brelish border. The monstrous nation of Droaam now claims the small city of Graywall.
This gateway to the kingdom of monsters is as deep into the barrens as most travelers are willing to go. The city was built using the strength of ogres and the architectural skills of medusas, all under the direction of Xor'chylic the mind flayer. The combination resulted in roughly formed buildings with an alien aesthetic that most visitors find disturbing.
I have written a few mandates and questions to help spark a campaign set in the border town of Graywall. My Eberron Resources blog post includes brief overviews and links to Eberron products that can help flesh out.
Mandates and Options
Someone must be a monster: You could be a monstrous humanoid or someone regarded as monstrous by the Five Nations. See my post for a list of available races.
Someone must be an agent: You could be an agent for one of the Dragonmarked Houses, a nation, one of the warlords of Droaam, Xor'chylic, or many others.
Someone must be a lifer: You have lived in the Droaam region before Breland withdrew from the region.
Each of you may have a dragonmark: The Wayfinder's Guide to Eberron includes the 5E rules for player characters with Dragonmarks.
Each player, tell me about your role, if any, in the Last War?
Lifer, tell me about your involvement in building Graywall?
Monster, tell me one way that you know that Droaam is not ready for other nations to acknowledge it's sovereignty?
Agent, tell me about a secret certain to get you in trouble.
One player, tell me about the half-orc you can trust amongst the House Tharask security detail for the human quarters?
One player, briefly describe and name an event that you saw when Xor'chylic showed its authority?
Two players, each tell me more about one person with whom you correspond. How often do you receive a message from them by way of the House Sivis outpost in Graywall?
One player, tell me about a crowd favorite at the arena in Graywallw.
One player, tell me a bit of the prophecy told to (and of?) you by Sora Teraza.
For starting an Eberron campaign, I would use a Session Zero. Given the depth and inter-connectedness of the Eberron Campaign Setting, as a Game Master I would want to ensure everyone has a common understanding.
I intend for the mandates, options, and questions to introduce both the local concerns and ideas of Graywall and some of the larger concepts in Eberron. These questions beg for further expansion; Who is Sora Teraza? What is House Sivis? Explain the Dragonmarked Houess?
To build these questions, I scoured the six paragraph entry of Graywall in the Eberron Campaign Setting (3e) and the larger Droaam entry.
update: I learned about “Backdrop Graywall” by Keith Baker in Dragon Magazine #368; I suppose I have more reading to do. In any campaign, I do not consider any written material canon until we bring it to the table.