Consider the following page from Kiniro Mosaic.
Some context, in case you don't know the series: The three girls are in high school. Karen is the blonde, Aya is the girl with black twin-tails, and Youko is the girl with short light hair. Karen is half-British, has never lived in Japan before, and still has some trouble with the language and culture. That's why she says "It might be something normal for you two Japanese people, but for someone like me, it was a big adventure."
It was shown earlier that Karen is pretty outgoing, but the joke here seems to be that Karen thinks going to a ramen shop is something that's only a big deal to her because she's foreign, and it turns out that it's also a big deal to natives Aya and Youko. But why do Aya and Youko consider this "amazing" and "grown-up"? Youko's line about fast food restaurants suggests there's some cultural reference concerning ramen shops that I'm missing.