Going to buy mugs with 〜に行く

Grammar Explanation: Going to for a purpose with 〜に行く

Cocoa discusses the café’s coffee cups with Chino.

ココア:: 「この前(まえ)面白(おもしろ)いカップ見(み)つけたんだ」; “I found an interesting cup the other day.”; 「今度(こんど)買(か)いに行(い)かない？」; “Why don't we go buy some?”; Literal: “Next time, won't we go for buying?”
リゼ:: 「へぇ　どんな」; “Oh? What kind?”

Key Points

1買(か)いに行(い)く states the purpose of going

2買(か)う uses its stem before に

買(か)う becomes 買(か)い, followed by purpose marker に and movement verb 行(い)く.

3行(い)かない is an invitation here

The negative question 今度(こんど)買(か)いに行(い)かない？ means “why don’t we go buy them sometime?”

4見(み)つけたんだ supplies background for the invitation

んだ explains why Cocoa proposes going shopping: she found an interesting cup earlier.

今度 (This time)

今度(こんど) means “this time” or “next time”, depending on context.

行く (To go)

行(い)く means to go or move toward a place away from the speaker.

どんな (What kind of)

どんな asks what kind of person or thing something is.