The Eastern Reaches were the lands to the east of Alagaësia, where Eragon went at the end of Inheritance.
The Riders' Exploration[]
During the Pre-Dragon War Era, the Riders explored many lands outside of Alagaësia. According to Heslant the Monk in Domia Abr Wyrda, the Riders had "programs of exploration, flying to the farthest reaches of land and water. Some of their discoveries were already familiar to the elves – who have preserved [both] maps and lore describing the continent from which they immigrated across the ocean – but the rest was as-yet uncharted territory". Although Galbatorix destroyed much of this knowledge, some information remained in Du Weldenvarden with the elves, and it is this information that reached Eragon during the Rider War.
Post–Rider War Era[]
After the end of the Rider War, Eragon Shadeslayer was unable to find a suitable home for the dragon eggs and Eldunarí he found on Vroengard, as well as for the Eldunarí previously enslaved by Galbatorix. He searched the land for a suitable home, but most locations were too close to the homes of the other races in Alagaësia. In the end, he and his dragon Saphira decided to leave Alagaësia for the East (It is mentioned earlier in Inheritance that Eragon had read of other lands outside of Alagaësia) with the precious objects. According to Eragon, they needed "physical barriers, cliffs, moats, and walls, too high for man, elf, dwarf, or Urgal to scale…the safety only distance can provide". According to the Eldunarí from Vroengard, there was another sea to the east, if they traveled far enough, but only empty lands between Alagaësia and the Eastern Sea. At this point, it is unknown how far exactly Eragon, Saphira, their treasures, and the contingent of elves that went with them traveled, although Christopher Paolini stated in an interview that the eastern coastline on the continent where Alagaësia is would be farther from the continent's west coast than if it was the United States' opposite coastlines.