How we cite our quotes: (Part.Paragraph)
Quote #1
And then it occurred to her that she was already feeling that she would need to remember this room, her sister, this scene, as though from a distance. (1.186)
Eilis is so nostalgic that she starts missing the past while it's still the present. Still, given that she'll be halfway across the planet (in an era, we must add, that you couldn't just use Snapchat or Skype to keep in touch), it's understandable that she's hesitant to leave the only home she's ever known.
Quote #2
What she would need to do in the days before she left and on the morning of her departure was smile, so that they would remember her smiling. (1.225)
Eilis is concerned with presenting a happy face so her family remembers her at her best. That's really thoughtful, and it shows that Eilis has a maturity well beyond her years. No matter how mature she might be, however, she's still totally unprepared for how this journey will change her as a person.
Quote #3
For the past few weeks, she realized, she had not really thought of home. The town had come to her in flashing pictures [...] but her own life [...] she had kept out of her mind. (2.54)
Interestingly, Eilis isn't actually homesick at first. Although she occasionally thinks about Ireland, she never dwells on her memories long enough to get truly bummed out. That's totally an effective strategy but, as we see here, it can only work for so long before all those memories start flooding back. And what's she supposed to do when that happens?