に行く details

write + go to do

kaki ni iku

go (somewhere) to do

meaning: go to write

昼ひるごはん、食たべに行いかない？

hirugohan, tabe ni ikanai?

Want to go grab lunch? casual

のど渇かわいたから、ちょっと飲のみ物ものを買いかいにいくね。

nodo kawaita kara, chotto nomimono o kai ni iku ne.

I'm thirsty, so I'll just go to buy a drink. casual

Examples

go to do — motion whose stated purpose is the verb

昼ひるごはん、食たべに行いかない？

hirugohan, tabe ni ikanai?

Want to go grab lunch? casual

のど渇かわいたから、ちょっと飲のみ物ものを買かいにいくね。

nodo kawaita kara, chotto nomimono o kainiiku ne.

I'm thirsty, so I'll just go to buy a drink. casual

週末しゅうまつはよく、友達ともだちと映画えいがを見みにいきます。

shuumatsu wa yoku, tomodachi to eiga o miniikimasu.

On weekends, I often go to see a movie with friends. neutral

午後ごご、取引先とりひきさきへ資料しりょうを届とどけに参まいります。

gogo, torihikisaki e shiryou o todoke ni mairimasu.

This afternoon I will go deliver the materials to our client. formal

The purpose slot works with the whole motion family — 飲みに来る, 取りに帰る, 遊びに出かける. する-nouns can skip the verb: 買い物に行く.

ために
Both answer "what for?", but に行く covers only purpose of movement with the goal verb reduced to its stem (買いに行く); ために takes any deliberate action and any main verb — 買うために並ぶ has no に行く equivalent.

ていく
One form apart on the same verb — 買いに行く states why you are going (purpose, masu-stem＋に), 買っていく says you buy and then move on or take it along (sequence, て-form); the stem choice, not 行く, carries the meaning.