В конце дня я отдыхаю дома.

Because конце is in the prepositional case, which is required after в when you talk about being in/at a place or moment (not movement towards it).

• конец (nominative) → в конце (prepositional) = at the end
• дня is genitive singular of день and is used after конец:
  
  • конец чего? – конец дня – the end of the day

So the structure is:

• в
  • конце (prepositional) + дня (genitive)
    = at the end of the day

Дня is the genitive singular form of день.

The word конец often takes the genitive to show “end of something”:

• конец дня – end of the day
• конец недели – end of the week
• конец месяца – end of the month

In Russian, you don’t use an extra word like “of”; instead, you change the noun to genitive case.

В конец дня is not natural in this context.

• в конец with the accusative is usually about movement to the end of something (e.g. to the end of the street).
• Here we are talking about a time period (at the end of the day), not movement.

So for time expressions like this, you normally use:

• в конце дня – at the end of the day (correct)

No, в конце дня here is literal: it means physically/temporally at the end of the day, in the evening or when the day finishes.

The English idiomatic “at the end of the day” = “ultimately” doesn’t match this Russian phrase in that figurative sense. For the idiomatic “ultimately”, Russians more often use things like:

• в итоге – in the end, ultimately
• в конечном счёте – ultimately, in the final analysis

Отдыхаю is the imperfective verb form, present tense, 1st person singular:

• я отдыхаю – I (am) rest(ing) / I relax / I take a rest (general, ongoing, repeated)

Отдохну is the perfective future:

• я отдохну – I will rest (once, as a completed action)

In В конце дня я отдыхаю дома, the speaker is describing a regular habit or a typical daily routine, so Russian uses the imperfective present: отдыхаю.

The infinitive is отдыхать – to rest, to relax (imperfective).

Conjugation (present tense):

• я отдыхаю – I rest / I relax
• ты отдыхаешь – you rest (sing., informal)
• он/она/оно отдыхает – he/she/it rests
• мы отдыхаем – we rest
• вы отдыхаете – you rest (pl. or formal)
• они отдыхают – they rest

Дома (with stress on the first syllable: до́ма) is an adverb meaning “at home”. It’s the standard way to say where you are when you mean your home as a general place:

• я дома – I am at home
• я отдыхаю дома – I rest at home

В доме literally means “in the house/building” and focuses on the interior of a building, not necessarily “my home” in the personal sense. For example:

• Он в доме – He is in the house (not outside)

In this sentence, дома = “at (my) home” is exactly what you want.

You could say я отдыхаю в доме, and it’s grammatically correct, but it sounds different:

• я отдыхаю дома – I rest at home (neutral, usual phrasing about your home).
• я отдыхаю в доме – I rest inside the house (as opposed to somewhere else, like outside, in the yard, etc.).

So в доме emphasizes being inside the building; дома emphasizes being at home as your place of residence.

Both are possible, but the neutral, most common word order is:

• я отдыхаю дома – subject → verb → place

Я дома отдыхаю is also correct, but it sounds a bit more emphatic, like you’re stressing where you rest:

• Я дома отдыхаю, а не в офисе. – I rest at home, not in the office.

Russian word order is relatively flexible, and changes usually affect emphasis, not grammatical correctness.

Yes, you can drop я, and many native speakers do in context when it’s clear who the subject is:

• В конце дня отдыхаю дома.

This sounds a bit more informal or diary-like, as if you’re casually listing what you do.

However, if you want a neutral, complete sentence, especially as a learner, keep the pronoun:

• В конце дня я отдыхаю дома.

It can mean both, depending on context:

• Right now / currently:

  • (On the phone) Ты где? – Я отдыхаю дома.
    – Where are you? – I’m resting at home.

• Habit / routine:

  • В конце дня я отдыхаю дома.
    – At the end of the day I (usually) rest at home.

Russian present imperfective often covers both present continuous and simple present meanings in English.

You can add каждый день:

• Каждый день в конце дня я отдыхаю дома.

Word order alternatives (all correct, just slightly different in rhythm/emphasis):

• В конце дня я каждый день отдыхаю дома.
• Каждый день я в конце дня отдыхаю дома.

The first version (Каждый день в конце дня я отдыхаю дома) is the most straightforward for learners.