Naći ćemo se u centru.

Because naći se is a set expression. Literally, it can mean to find oneself, but in everyday Serbian it very often means to meet up.

So:

• naći = to find
• naći se = to meet, to meet up, to find oneself somewhere

In this sentence, Naći ćemo se u centru, the natural meaning is We’ll meet in the center / downtown.

This is the future I tense in Serbian.

It is made with:

• the infinitive of the main verb: naći
• the short form of hteti = ćemo for we will

So:

• naći = to meet / to find
• ćemo = we will

Together: naći ćemo = we will meet / we will find

With se, it becomes naći ćemo se = we will meet.

In Serbian, future forms with verbs ending in -ći are written separately:

• naći ćemo
• doći ćemo
• reći ćemo

That is standard spelling.

With many verbs ending in -ti, Serbian often writes the future as one word:

• radiću
• videću
• uradićemo

But with -ći verbs, it stays separate, so naći ćemo is correct.

Se is a reflexive particle. In this sentence, it is part of the verb expression naći se.

You should learn naći se as a whole unit, because its meaning is different from plain naći.

Compare:

• naći nekoga/nešto = to find someone/something
• naći se = to meet up / to find oneself somewhere

So se is necessary here. Without it, the sentence would mean something different.

Because Serbian usually does not need the subject pronoun when the verb already shows the person.

Here, ćemo tells you that the subject is we.

So:

• Naći ćemo se u centru. = We’ll meet in the center.
• Mi ćemo se naći u centru. = also correct, but mi is added only for emphasis or contrast

Serbian often leaves pronouns out unless they are needed.

Because u can take different cases depending on the meaning:

• u + accusative = motion into something
• u + locative = being in a place

Here the meaning is location: the meeting will happen in the center, not movement into the center. So Serbian uses the locative:

• u centru = in the center

Compare:

• Idemo u centar. = We are going to the center.
• Naći ćemo se u centru. = We will meet in the center.

Because centru is the locative singular form of centar.

Dictionary form:

• centar = center

After u for location, it changes to locative:

• u centru = in the center

This kind of change is very common in Serbian noun declension. A masculine noun often changes its ending depending on its role in the sentence.

Very often, yes.

In everyday speech, u centru commonly means downtown or in the city/town center. The exact meaning depends on context.

It can also literally mean in the center of something, but if people are making plans, u centru usually means in the central part of town.

Yes. Serbian word order is fairly flexible, though some versions sound more neutral than others.

The most neutral version here is:

• Naći ćemo se u centru.

You could also say:

• Mi ćemo se naći u centru.
• U centru ćemo se naći.

These all mean basically the same thing, but the emphasis changes:

• Naći ćemo se u centru. = neutral
• Mi ćemo se naći u centru. = emphasizes we
• U centru ćemo se naći. = emphasizes in the center

Because this sentence refers to a single completed future event: one planned meeting.

In Serbian, perfective verbs are very common for one-time future actions that will be completed:

• Naći ćemo se... = We’ll meet up...

That sounds natural because the meeting is seen as one whole event.

If you wanted a repeated or habitual idea, Serbian would usually use a different verb or structure.

A rough English-friendly guide is:

NA-chee CHE-mo se oo TSEN-troo

A few pronunciation notes:

• ć is a soft sound, somewhat like a very soft ch
• č is harder than ć, but there is no č in this sentence
• c in centru sounds like ts
• u is pronounced like oo

So:

• Naći ≈ NA-chee
• ćemo ≈ CHE-mo
• centru ≈ TSEN-troo

Yes, that is also natural.

• Naći ćemo se u centru. = We’ll meet up in the center.
• Srešćemo se u centru. = We’ll meet in the center.

The difference is slight:

• naći se often suggests an arranged meeting or meeting up
• sresti se also means to meet, and can sound a little more like the actual encounter

In many everyday situations, both work well.