How to Find an End City in Minecraft (and Get Elytra)

Quick answer

Beat the dragon, then throw an Ender pearl into the small End gateway portal.
Look for tall purple towers made of purpur and end stone bricks.
Elytra are only found on end ships, which some cities have.

End cities are where you get elytra and shulker boxes. They're far from the main island, so you need the gateway to get there.

Waypoint ManagerSave Minecraft waypoints across your worlds

Getting to the outer islands

Kill the Ender Dragon. A small gateway portal appears near the edge of the main island.
The gateway is too small to walk into. Throw an ender pearl into it.
You land on the outer islands. If you land on a tiny island, bridge or pearl across to a bigger one.

Mind the voidFalling off the islands means losing everything you carry. Sneak at edges and carry blocks.

Spotting a city

End cities are tall towers built from Purpur block and End stone bricks, usually on flat ground among chorus trees. Some have banners hanging from the top.

You may have to travel thousands of blocks to find one, so save every city you find.

Shulkers

Shulkers hide in boxes on the walls and fire bullets that make you float. Kill them for Shulker shell items, which craft into shulker boxes.

Shield upA shield blocks shulker bullets. Slow falling or milk helps if you start floating off an edge.

End ships and elytra

A city can have at most one end ship, floating next to a bridge. Many cities have none.

The elytra sit in an item frame inside the ship, the only place to get them in survival.
The Dragon head is on the front of the ship.
Two treasure chests sit inside, guarded by a shulker.