Ей хочется посидеть в тихом парке после работы.

Because хочется is an impersonal form, and the person experiencing the feeling goes in the dative case.

• ей = to her
• хочется = it is wanted / she feels like

So Ей хочется посидеть... means something like:

• She feels like sitting...
• She would like to sit...

This is a very common Russian pattern for talking about a desire that feels more like an internal urge or mood.

Compare:

• Она хочет посидеть в парке. = She wants to sit in the park.
• Ей хочется посидеть в парке. = She feels like sitting in the park.

The second version often sounds a bit softer, more personal, and more like being in the mood for something.

Хочется is the 3rd person singular impersonal form of хотеться, which means:

• to feel like
• to want in a more spontaneous or emotional sense

It is different from хотеть, which is the normal verb to want.

A useful contrast:

• Я хочу спать. = I want to sleep.
• Мне хочется спать. = I feel sleepy / I feel like sleeping.

So in your sentence, Ей хочется suggests a feeling arising in her, not just a neutral statement of intention.

Because with impersonal words like хочется, the person who experiences the state is usually put in the dative.

So:

• я → мне
• ты → тебе
• она → ей
• он → ему
• мы → нам

Examples:

• Мне хочется кофе. = I feel like having coffee.
• Ему хочется домой. = He feels like going home.
• Ей хочется посидеть в тихом парке. = She feels like sitting in a quiet park.

This is very common in Russian with expressions of feeling, need, and mood.

Посидеть is the perfective form, and here it usually means to sit for a while.

Compare:

• сидеть = to sit, to be sitting (imperfective)
• посидеть = to sit for a while (perfective)

In this sentence, посидеть suggests a limited, complete little activity: she wants to spend some time sitting in the park.

So:

• Ей хочется сидеть в парке would sound more like focusing on the ongoing state of sitting.
• Ей хочется посидеть в парке sounds more natural if you mean she feels like sitting there for a bit.

The prefix по- often gives this idea of doing something for a short time.

Because Russian often uses this structure:

[dative person] + хочется + infinitive

It means someone feels like doing something.

Pattern:

• Мне хочется спать. = I feel like sleeping.
• Ему хочется поесть. = He feels like eating.
• Ей хочется посидеть в тихом парке. = She feels like sitting in a quiet park.

So посидеть is the action she feels like doing.

Because after в meaning in, when talking about location, Russian uses the prepositional case.

So:

• парк → в парке
• тихий парк → в тихом парке

Both the noun and its adjective must match in case, gender, and number.

Here:

• парке = prepositional singular of парк
• тихом = prepositional singular masculine/neuter of тихий

So в тихом парке means in a quiet park.

Because adjectives change to agree with the noun they describe.

The noun парк is:

• masculine
• singular
• in the prepositional case

So the adjective must also be:

• masculine
• singular
• prepositional

That gives:

• тихий → тихом

A few similar examples:

• в большом доме = in a big house
• в красивом городе = in a beautiful city
• в тихом парке = in a quiet park

Because the preposition после always takes the genitive case.

So:

• работа → после работы = after work
• урок → после урока = after the lesson
• обед → после обеда = after lunch

So in your sentence:

• после работы = after work

This is a fixed and very common case pattern.

Here it most naturally means work in the general sense, as in after work / after finishing work for the day.

Russian often uses a noun without an article, because Russian has no articles like a or the.

So после работы can be understood from context as:

• after work
• after her work
• after the work

In this sentence, the natural English translation is simply after work.

В means in here and shows location.

So:

• в парке = in the park

This is different from motion toward a place, although Russian also often uses в for that. The case tells you the difference:

• в парк = into the park / motion toward it
• в парке = in the park / location

In your sentence, she wants to sit in the park, so the location form в парке is used.

The word order is natural, but Russian word order is more flexible than English.

Ей хочется посидеть в тихом парке после работы is a neutral, normal order.

You could move things around for emphasis, for example:

• После работы ей хочется посидеть в тихом парке.
  Emphasis on after work.

• В тихом парке ей хочется посидеть после работы.
  More emphasis on in a quiet park.

The basic meaning stays the same, but the focus changes slightly.

Not naturally in English, but that kind of literal breakdown can help you understand the grammar.

A rough structural breakdown is:

• Ей = to her
• хочется = it is desired / she feels like
• посидеть = to sit for a while
• в тихом парке = in a quiet park
• после работы = after work

So a very literal gloss might be:

• To her, it feels desirable to sit for a while in a quiet park after work.

But natural English would be:

• She feels like sitting in a quiet park after work.
• She’d like to sit in a quiet park after work.