What problem do you have with it?

It's nonsensical and an actual error for one. ;)

If you search for "来週は学校に行きません" on Google this thread is the only result.

The reason for this is contextual (internet posts), not grammatical. You'll get more results if you remove the polite ending and/or the topic particle (try "来週学校に行かない").

Actually, since not wanting to go to school is a common sentiment, it can end up simplified into something with no particles at all: https://twitter.com/k_y02240/status/613690896916201472

I hope you don't find it nonsensical, though, I understood it just fine.

And checking ghits for plain forms shows:

"学校に行く" - 3,680,000

"学校へ行く" - 444,000

so I think the other way is actually the variant!

BTW, I feel like "学校に行く" - where に means "for/into" - has a sense of "going to school to go to class", but "学校へ行く" - where へ means "towards" - has a sense of "going to the school building as a physical place".

Here's a forum thread about it:

http://oshiete.goo.ne.jp/qa/5458812.html

It is neither nonsensical nor an error.

    来週は学校に行きません

 roughly translates as "Next week, I won't go for school."

The correct usage is

    来週は学校*へ*行きません

"Next week, I won't go to school."

Hi, I'm a gainfully employed translator of Japanese and linguist.

Short answer: the sentence is fine as it stands, although your alternative is equally grammatical (if less idiomatic - "学校へ行かない" gets about 1/4 of the ghits of "学校に行かない" by my count, and personally I'd never use へ).

Long answer: Japanese draws a distinction between verbs of A→B movement (e.g. 行く to go; 引っ越す to move house; 移動する to move/change location) and verbs that describe the manner of motion (e.g. 歩く to walk; 走る to run). The A→B verbs can happily take an indirect object complement (a に phrase) as the destination, because there's really no other possible meaning. You can't "go for school", as you put it.

Verbs of motion, on the other hand, are less flexible. These can't take an indirect object complement, and need a more expressly destinatory case (think へ、へと、まで). The reason for this is that a change of location is not implied in the verb, however counterintuitive that might seem to an English speaker.

Interestingly, motion verbs can take a direct object (を), such as in 街を歩く 'to walk around town'. Another indication that they're not strictly destinatory. Also they can take adverbs that further qualify motion, such as ぽつぽつ歩く 'to dawdle/mosey/toddle'(? tough to translate), whereas 行く can't. A→B verbs can however take adverbs that qualify the speed, like ゆっくり行く 'to go unhurriedly' - but this is different from ゆっくり歩く 'to walk in a slow manner'.

This is my first ever comment on HN so I've tried to be as informative as possible... If you have any counterexamples I'd be happy to try to explain them.

Japanese N1 and JETRO biz japanese here.

Yeah sure, in vernacular construct, which explains more Google results.

Just stop. You're embarrassing yourself.

Entirely false. に is perfectly valid here.

There is nothing wrong with that sentence.