Obići ćemo znamenitost i svratiti na vidikovac.

Because Serbian often leaves the subject pronoun out when the verb already shows who the subject is.

Here, ćemo marks 1st person plural in the future tense, so the sentence already means we will...
You could add mi for emphasis:

Mi ćemo obići znamenitost i svratiti na vidikovac.

But in normal speech, mi is usually unnecessary.

Ćemo is the future-tense auxiliary, from the verb hteti (to want), used to build the Serbian future.

So:

• obići ćemo = we will visit / go around
• svratiti is also understood as part of that same future idea

A simple way to think of it is:

• ćemo = will for we

In standard Serbian, ćemo is a clitic, which means it usually does not stand at the very beginning of the clause.

So if there is no expressed subject like mi, the infinitive often comes first:

Obići ćemo...

If you do include the subject, then you can say:

Mi ćemo obići...

Both are normal, but Obići ćemo... is a very common and natural structure.

Because Serbian future tense is commonly formed with:

• a future auxiliary like ću, ćeš, će, ćemo, ćete, će
• plus the infinitive

So here:

• obići ćemo = we will visit
• svratiti stays in the infinitive because it is also governed by the future auxiliary

This is different from English, where the main verb stays in a base form after will.

Because one future auxiliary can apply to both verbs when they are linked by i (and).

So:

Obići ćemo znamenitost i svratiti na vidikovac.

naturally means:

We will visit the landmark and stop by the viewpoint.

Repeating ćemo is usually unnecessary. Serbian often avoids repetition when the meaning is already clear.

Obići literally has the idea of going around something, but in travel contexts it very often means:

• to visit
• to see
• to tour

So in this sentence, it does not necessarily mean physically circling the landmark. It more likely means to go see it / visit it as a sight.

Also, obići is perfective, so it presents the action as a completed whole.

Not exactly. Svratiti usually means something like:

• to stop by
• to drop in
• to make a short stop
• to make a quick detour

So svratiti na vidikovac suggests a brief visit to the viewpoint, not simply going there as the main destination.

It also sounds a bit lighter and more casual than a plain go verb.

Because Serbian has no articles.

English needs a landmark or the landmark, but Serbian simply says:

znamenitost

The exact meaning depends on context:

• a landmark / a sight
• the landmark / the sight

So learners from English often notice that Serbian leaves this information unstated unless the context makes it clear.

Because na is used here to show movement toward a destination.

With verbs of motion, Serbian often uses:

• na + accusative for movement to a place
• na + locative for being at that place

So:

• svratiti na vidikovac = to stop by / go to the viewpoint
• biti na vidikovcu = to be at the viewpoint

For vidikovac, na is the natural preposition, not u.

Because the sentence describes a plan made up of single, completed actions:

• obići = visit the sight as one whole event
• svratiti = make one stop at the viewpoint

That is why perfective verbs fit so well here. They match the idea of an itinerary:

• first we will do this,
• then we will do that.

If imperfective verbs were used instead, the sentence would feel more ongoing, repeated, or less neatly bounded.

Yes, Serbian word order is fairly flexible, although not completely free.

This version is very natural:

Obići ćemo znamenitost i svratiti na vidikovac.

But other versions are also possible for emphasis, such as:

• Mi ćemo obići znamenitost i svratiti na vidikovac.
• Znamenitost ćemo obići i svratiti na vidikovac.

The main thing to remember is that the clitic ćemo usually does not begin the sentence by itself.