Knowledge:
We can't possibly write out a suitable ending unless we list what we know based on the final chapters of Inheritance. So, let us compile a list of what we know based on the events that transpired from the death of Galbatorix up to the end of the novel.
-Teirm is an independent city-state allied with the current empire
-Arya is the remaining confirmed Rider still in Alagaesia (with a dragon named Firnen), in addition to being Queen of the Elves.
-Murtagh is somewhere in the north
-Murtagh and Nasuada harbor feelings for each other
-Nasuada is the new queen
-Roran is Earl of Palancar Valley
-The Urgals and Dwarves were added to the enchantment that binds Riders to Dragons
-Katrina and Roran have a baby girl named Ismira
-Sloan can see again, but still can't show his face anywhere near Roran and Katrina
-Jeod and Helen possess a gigantic trading empire based in Ilirea
-Surda doubles its size, gaining Aroughs, Feinster, Melian, Belatona, and the isles to the south
-The Priests of Helgrind are gone
-Ra'zaac eggs may still exist somewhere in Alagaesia
-Eragon departs to the east with Blodhgarm and a few other elves, in possession of the Eldunari and the remaining dragon eggs
If I have forgotten anything or if any information is inaccurate, please correct the problem as soon as possible.