После работы мне хочется ненадолго выйти на балкон.

Because после requires the genitive case.

• работа = work, job
• genitive singular: работы

So:

• после работы = after work

This is a very common pattern:

• после урока = after the lesson
• после обеда = after lunch
• после фильма = after the movie

Мне is the dative case of я.

In this sentence, Russian does not say I want in the most direct way. Instead, it uses a structure more like:

• мне хочется = it is desirable to me / I feel like / I want to

So мне shows the person who experiences the feeling.

Compare:

• я хочу = I want
• мне хочется = I feel like / I have the urge to / I’d like to

The second one often sounds a bit softer, more personal, or more about a spontaneous feeling.

Both can be translated as want, but they are not identical.

я хочу

This is the straightforward, neutral way to say I want.

• После работы я хочу выйти на балкон. = After work I want to go out onto the balcony.

мне хочется

This often means:

• I feel like
• I have a desire to
• I’d like to

It can sound a little less direct and more emotional or spontaneous.

So:

• мне хочется ненадолго выйти на балкон suggests a feeling like I feel like stepping out onto the balcony for a little while.

Because хочется is part of an impersonal construction.

In this pattern, Russian does not make I the grammatical subject. Instead, the desire is expressed impersonally:

• мне хочется = literally something like it wants itself to me, though this is not natural English

The important thing is to learn it as a fixed pattern:

• мне хочется спать = I feel sleepy / I want to sleep
• тебе хочется есть? = Do you feel like eating?
• ему хочется домой = He feels like going home

So even though the meaning involves I, the grammar works differently from English.

Ненадолго means for a short time, briefly, or not for long.

It is built from:

• надолго = for a long time
• не-
  • надолго = not for long

So:

• выйти ненадолго = to step out for a little while

Examples:

• Я отойду ненадолго. = I’ll step away for a short time.
• Он приехал ненадолго. = He came for a short visit.

Выйти is the perfective form, while выходить is imperfective.

Here, выйти fits because:

The sentence refers to one complete action:

• stepping out onto the balcony once

So:

• выйти на балкон = to go/step out onto the balcony once

Compare:

• Мне хочется выйти на балкон. = I feel like stepping out onto the balcony.
• Я люблю выходить на балкон по вечерам. = I like going out onto the balcony in the evenings.

The second sentence describes a repeated or habitual action, so выходить is more natural there.

The prefix вы- often gives the idea of out or going out.

So:

• идти = to go, to be going
• выйти = to go out, to step out

In this sentence:

• выйти на балкон = to go out onto the balcony

The idea is that the speaker is inside and wants to move outward, onto the balcony.

Russian uses на with балкон when talking about movement onto the balcony.

Movement toward a place:

• на балкон = onto the balcony

Location at a place:

• на балконе = on the balcony

So:

• выйти на балкон = to go out onto the balcony
• стоять на балконе = to stand on the balcony

В балкон is not correct here, because a balcony is treated as a surface/platform-like place in Russian, not as something you go into.

This is similar to:

• идти на улицу = go out onto the street
• быть на улице = be outside / on the street

Because after на with movement, Russian often uses the accusative case, and for many masculine inanimate nouns, the accusative singular looks exactly like the nominative singular.

• nominative: балкон
• accusative: балкон

So:

• на балкон = onto the balcony

Compare with location:

• на балконе = on the balcony

There the noun is in the prepositional case.

Yes, absolutely.

That sentence is fully natural and means nearly the same thing. The main difference is tone:

• я хочу = more direct, straightforward
• мне хочется = softer, more like I feel like

So both are correct:

• После работы мне хочется ненадолго выйти на балкон.
• После работы я хочу ненадолго выйти на балкон.

The first one often sounds a little more natural if you are describing a current mood or craving.

Yes, Russian word order is fairly flexible, though different orders can slightly change emphasis.

The original sentence:

• После работы мне хочется ненадолго выйти на балкон.

is a very natural neutral order.

Other possible versions:

• Мне после работы хочется ненадолго выйти на балкон.
  • slightly emphasizes after work
• Ненадолго мне хочется выйти на балкон после работы.
  • possible, but less neutral and more marked
• На балкон мне хочется выйти после работы.
  • emphasizes onto the balcony

So the original is a good default version for learners.

Usually it means after work in the general everyday sense, not necessarily after the work as a specific task.

So in this sentence, it most naturally means:

• after finishing work
• after the workday

If you wanted to refer to some specific piece of work, the context would usually make that clear.

You would usually add a purpose phrase.

For example:

• После работы мне хочется ненадолго выйти на балкон подышать свежим воздухом. = After work I feel like stepping out onto the balcony to get some fresh air.

• После работы мне хочется ненадолго выйти на балкон покурить. = After work I feel like stepping out onto the balcony to smoke.

This shows how Russian often adds another infinitive after a verb of motion to express purpose.

The main stresses are:

• послé
• рабóты
• мне
• хóчется
• ненадóлго
• выйти
• балкóн

A rough pronunciation guide:

• Послé рабóты мне хóчется ненадóлго вый-ти на балкóн.

One thing learners often notice is that хочется is pronounced with the stress on the first syllable: хóчется.