How we cite our quotes: (Chapter.Paragraph)
Quote #1
Eragon swayed blearily and said, "It's good to be back." […] Home. For the first time since before the hunt, he relaxed completely as sleep overtook him. (2.86)
You know how when you go away from home for a while, it just feels really good to be back? Things seem to make more sense to you, you know where everything is, and you just feel more relaxed. Well, that's how Eragon feels when he gets back from the hunt. Just imagine how he feels, then, when he loses his home in the Ra'zac attack.
Quote #2
"This is a small village hidden by mountains. It's not surprising that you've escaped notice. However, I wouldn't expect that to last." (3.53)
As Merlock points out here, Eragon's home is sheltered from the wider world. But not for long—the world comes knocking, and he's forced to leave that shelter behind.
Quote #3
Mother, aunt, uncle—he had lost them all. The weight of his grief was crushing, a monstrous force that left him tottering. (13.5)
After Garrow dies, we're reminded, through Eragon's grief, how much our sense of home is due to the people that inhabit it. If that tired old saying has any truth, and home is indeed "where the heart is," then a large part of Eragon's heart is with his family members who he's tragically lost.