שכר הדירה בדירה הזאת גבוה יותר, אבל המקום שקט יותר.

This is a construct chain (called סמיכות in Hebrew).

• שכר = payment / wage
• דירה = apartment
• שכר דירה = apartment rent, i.e. rent

When a construct chain is definite, the definiteness usually shows up on the second noun, not the first one.

So:

• שכר דירה = rent
• שכר הדירה = the rent

That is why you do not say השכר הדירה here.

In Hebrew, the verb to be is usually not expressed in the present tense.

So:

• שכר הדירה ... גבוה יותר
  literally looks like the rent ... higher
• but it means the rent ... is higher

The same thing happens in:

• המקום שקט יותר = the place is quieter

This is completely normal Hebrew.

Because ב־ means in.

So:

• דירה הזאת would be trying to say this apartment (and even that form would need adjustment; see below)
• בדירה הזאת means in this apartment

Also, in fully pointed Hebrew, this is really:

• בַּדירה הזאת

That is ב + ה + דירה compressed together:

• ב־ = in
• הדירה = the apartment
• בַּדירה = in the apartment

So בדירה הזאת = in this apartment.

In Hebrew, demonstratives like this and that usually come after the noun.

So Hebrew says:

• הדירה הזאת = this apartment
• literally: the apartment this

This is one of the most common word-order differences from English.

In your sentence, because of the preposition ב־:

• בדירה הזאת = in this apartment

Because דירה is a feminine singular noun.

Hebrew demonstratives must agree with the noun in gender and number.

• masculine singular: הזה
• feminine singular: הזאת

So:

• הספר הזה = this book
• הדירה הזאת = this apartment

Since דירה is feminine, הזאת is the correct form.

Because they agree with the nouns they describe:

• שכר is masculine singular → גבוה יותר
• מקום is masculine singular → שקט יותר

A common mistake is to look at דירה and think גבוהה should be used, but גבוה is describing שכר הדירה (the rent), not the apartment.

So:

• שכר הדירה גבוה יותר = the rent is higher
  not because דירה is feminine, but because שכר is masculine

Yes. A very common way to make a comparative in Hebrew is:

• adjective + יותר

So:

• גבוה יותר = higher
• שקט יותר = quieter

Unlike English, Hebrew does not usually add an ending like -er to the adjective.

It just uses יותר = more.

So literally:

• גבוה יותר = high more
• שקט יותר = quiet more

but in natural English we translate those as higher and quieter.

Because this sentence is making a comparison implicitly, not with a full than... phrase.

It says:

• the rent is higher
• but the place is quieter

The listener is expected to understand: higher and quieter than the other option being discussed.

If Hebrew wants to say than explicitly, it often uses מ־.

For example:

• שכר הדירה גבוה יותר מהדירה הקודמת
  = the rent is higher than in the previous apartment

So the sentence is complete even without saying than.

המקום literally means the place.

In context, it can refer to:

• the apartment
• the property
• the area/environment around it

Using המקום can sound a little broader than just הדירה. It suggests not only the apartment itself, but the overall place.

So:

• אבל המקום שקט יותר = but the place is quieter

You could also say:

• אבל הדירה שקטה יותר

That would mean more specifically but the apartment is quieter.

A simple transliteration is:

skhar ha-dira ba-dira ha-zot gavoha yoter, aval ha-makom shaket yoter

A few helpful notes:

• שכר starts with a consonant cluster, something like skhar
• דירה = di-RA
• הזאת = ha-ZOT
• גבוה = ga-VO-a / ga-VO-ha
• שקט = sha-KET
• אבל = a-VAL

So the rhythm is roughly:

skhar ha-dira ba-dira ha-zot ga-VO-a yo-TER, a-VAL ha-ma-KOM sha-KET yo-TER