Na kraju smo se odlučili za mali apartman blizu centra.

Yes, literally na kraju means at the end, but in this sentence it works more like in the end, finally, or after considering everything.

So:

• na kraju = in the end / finally
• It often introduces the final result of a decision or process.

Examples:

• Na kraju smo ostali kod kuće. = In the end, we stayed home.
• Na kraju je sve bilo dobro. = In the end, everything was fine.

In your sentence, it signals that some choosing or comparing probably happened before the final decision.

Smo se odlučili is the perfect tense of the verb odlučiti se.

It is built like this:

• smo = we are / we have (auxiliary from biti)
• odlučili = past participle
• se = reflexive particle

So the structure is:

• smo se odlučili = we decided

Croatian commonly uses this kind of past tense to talk about completed actions.

Breakdown:

• ja sam se odlučio / odlučila
• ti si se odlučio / odlučila
• mi smo se odlučili / odlučile

So the sentence is using a normal past-tense pattern.

Here, se is part of the verb itself. The usual expression for to decide in the sense of make up one’s mind / choose is odlučiti se.

So:

• odlučiti se za nešto = to decide on something
• odlučiti without se can exist, but it usually works differently and often means to determine, to settle, or is used in other structures.

In this sentence, se is necessary because the meaning is:

• we decided on a small apartment

So:

• odlučili smo se za mali apartman = correct
• odlučili smo za mali apartman = not correct in standard Croatian

Because Croatian says:

• odlučiti se za + accusative = to decide on / to opt for

This is a fixed pattern you should learn as a whole expression.

Examples:

• Odlučili smo se za hotel. = We decided on a hotel.
• Odlučila se za plavu haljinu. = She chose the blue dress.
• Odlučio sam se za vlak. = I opted for the train.

So in your sentence:

• za mali apartman = for a small apartment
• together: odlučili se za mali apartman = decided on a small apartment

Because za here requires the accusative case, and apartman is a masculine singular inanimate noun.

For masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: mali apartman
• accusative: mali apartman

That is why nothing visibly changes.

If it were a feminine noun, you would see a clearer change:

• za malu sobu = for a small room

So in your sentence:

• za + accusative
• mali apartman happens to look the same as nominative

Because blizu requires the genitive case.

So:

• blizu + genitive = near / close to

Examples:

• blizu škole = near the school
• blizu mora = near the sea
• blizu centra = near the center

The noun centar changes in the genitive singular to centra.

So:

• nominative: centar
• genitive: centra

That is why blizu centra is correct.

Yes. Blizu centra is describing apartman.

So the structure is:

• za mali apartman = for a small apartment
• blizu centra = near the center

Together:

• za mali apartman blizu centra = for a small apartment near the center

It works much like English, where near the center comes after the noun and gives extra information about it.

In the Croatian past tense, the participle agrees with the gender and number of the subject.

For we:

• odlučili = masculine plural, or mixed-gender group, or sometimes the default when at least one male is included
• odlučile = feminine plural

So:

• Mi smo se odlučili... = We decided...
  used for a group of men, or a mixed group
• Mi smo se odlučile... = We decided...
  used if the speakers are all female

Because the sentence has odlučili, the speakers are either:

• male, or
• mixed-gender

Croatian word order is fairly flexible, but small words like smo and se are clitics, and they tend to appear in a special position near the beginning of the clause.

That is why the neutral sentence is:

• Na kraju smo se odlučili za mali apartman blizu centra.

This sounds natural and standard.

You may also hear other word orders for emphasis, but not every rearrangement sounds equally natural. For learners, it is best to remember this pattern:

• time/expression first: Na kraju
• then clitics: smo se
• then the main verb: odlučili
• then the rest: za mali apartman blizu centra

So smo se is not random—it follows a common clitic-placement rule.

Not exactly, though they can overlap.

• stan usually means apartment / flat in a general everyday sense
• apartman often suggests a holiday apartment, rental unit, or a place presented as a separate accommodation, sometimes a bit more commercial or tourist-oriented

So:

• mali stan = a small apartment/flat
• mali apartman = a small apartment, often with a rental or accommodation feel

In many contexts, both can be translated as apartment, but the nuance may differ.

Yes, odlučiti se is perfective.

That means it refers to a completed decision: the decision was made.

Its imperfective partner is usually:

• odlučivati se

Compare:

• Dugo smo se odlučivali. = We were deciding for a long time.
• Na kraju smo se odlučili za mali apartman. = In the end, we decided on a small apartment.

So in your sentence, the perfective verb is exactly right because it talks about the final completed choice.