kinyuusuru basyo ga nakanaka mitukaranakute, kakariin ni kiita

Because Japanese puts modifying clauses before the noun they describe.

So 記入する場所 is literally [fill in/write] + place, meaning the place where you fill it in or a place to fill it out.

English uses words like where, that, or to:

• the place where I write
• a place to fill it out

Japanese does not need those words here.

In Japanese noun-modifying clauses, the noun at the end is understood as playing some role inside the clause, and that role is usually inferred from context.

Here, 場所 is understood as the place related to 記入する. English makes that relationship explicit with where or to, but Japanese usually does not.

So:

• 記入する場所 = a place where you fill it in

You do not say 記入するの場所 here.

記入する is a more formal word that means to fill in, to enter information, or to write something in the proper place, especially on a form, application, or document.

書く is the general verb to write.

So:

• 名前を書く = write your name
• 申込書に記入する = fill in an application form

In this sentence, 記入する sounds natural because the situation is probably about filling out a form or document.

Because the verb here is 見つかる, not 見つける.

見つかる is an intransitive verb, so the thing that is found takes が:

• 場所が見つからない = the place cannot be found / I can't find the place

If you used the transitive verb 見つける, you would normally use を:

• 場所を見つけられない = I can't find the place

So が is there because 場所 is the thing that isn't being found.

This is a very common pair:

• 見つける = to find something
• 見つかる = to be found, to turn up

Compare:

• 鍵を見つけた = I found the key
• 鍵が見つかった = the key was found / turned up

In this sentence, 見つからなくて focuses less on the speaker's active searching and more on the result: a place wasn't available / didn't turn up easily.

With a negative verb, なかなか usually means:

• not easily
• not readily
• hard to

So:

• なかなか見つからない = can't find it easily, it's hard to find

This is a very common pattern:

• なかなか分からない = I don't understand it easily
• なかなか終わらない = it doesn't finish easily / it takes a long time

It comes from 見つかる:

1. 見つかる = dictionary form
2. 見つからない = negative form
3. 見つからなくて = -te form of the negative

So the pattern is:

• verb + ない
• then change ない to なくて

Examples:

• 行かない → 行かなくて
• 分からない → 分からなくて
• 見つからない → 見つからなくて

It links the first part of the sentence to the second part.

Here, it connects:

• 記入する場所がなかなか見つからなくて to
• 係員に聞いた

In context, -なくて most naturally shows reason/cause:

• because I couldn't find a place to fill it out, I asked a staff member

It can sometimes just mean and, but here because is the most natural reading.

Because when 聞く means to ask, the person you ask is commonly marked with に.

So:

• 係員に聞いた = asked a staff member

If you want to mention what you asked, that part can be added separately:

• 係員に場所を聞いた = asked the staff member where the place was / asked the staff member about the place

Also, 係員 means something like staff member, attendant, or clerk, depending on the situation.

Japanese often leaves out information that is obvious from context.

Two things are omitted here:

1. After 記入する, the thing being filled in is not stated.
   It could be something like:

   • a form
   • an application
   • a document

2. After 聞いた, what was asked is also omitted.
   It is understood to be something like:

   • where I could fill it in
   • where the writing area was
   • where the form-filling place was

So the sentence sounds natural even though some details are unstated.

This sentence is written in the plain style.

• 聞いた = plain past
• 聞きました = polite past

The plain style is very common in:

• textbooks
• example sentences
• casual speech
• written narration

It does not make the meaning less correct. It just changes the level of politeness. A polite version would be:

記入する場所がなかなか見つからなくて、係員に聞きました。