Post la kunveno ni serĉis kafejon ĉie en la centro.

Because -is is the Esperanto past-tense ending.

• serĉi = to look for, to search for
• serĉas = look for / am looking for
• serĉis = looked for / were looking for
• serĉos = will look for

So ni serĉis means we looked for or we were looking for.

The -n marks the direct object.

In this sentence, the thing being looked for is kafejo (a café / coffee shop), so it becomes:

• kafejo = a café
• kafejon = a café, as the direct object

Esperanto usually marks the direct object with -n, regardless of word order.

So:

• Ni serĉis kafejon = We looked for a café.

Because the sentence does not mean a specific, already-known café. It means a café, not the café.

In Esperanto:

• la kafejo = the café
• kafejo = a café / café in a general sense

Since they were just trying to find any suitable café, Esperanto leaves out la.

Post is a preposition meaning after.

So:

• post = after
• la kunveno = the meeting

Together, post la kunveno means after the meeting.

There is no extra word like English of needed here. Esperanto prepositions connect directly to the noun phrase.

Because it refers to a specific meeting that both speaker and listener can identify.

In Esperanto, la is used much like English the:

• kunveno = a meeting
• la kunveno = the meeting

So post la kunveno means after the meeting, probably one already mentioned or understood from context.

Kunveno is the noun for meeting or gathering.

It is built from common Esperanto parts:

• kun- = together
• ven = come
• -o = noun ending

So the idea is something like a coming together.

This kind of word-building is very common in Esperanto.

Ĉie means everywhere.

So:

• ĉie = everywhere
• en la centro = in the center / downtown

Together, ĉie en la centro means everywhere in the center or all over downtown.

It tells you that they searched in many places throughout that area, not just in one spot.

Because the two words do different jobs:

• ĉie tells you the search was widespread: everywhere
• en la centro tells you the area: in the center

So the meaning is not just everywhere in a general sense, but specifically everywhere in the city center / downtown area.

It can mean either, depending on context.

In a sentence like this, a learner will often understand la centro as:

• the center of town
• the city center
• downtown

So ĉie en la centro would naturally suggest searching around the central part of town.

Yes. Esperanto word order is fairly flexible because grammar roles are marked clearly, especially by the -n on the direct object.

For example, these are possible:

• Post la kunveno ni serĉis kafejon ĉie en la centro.
• Ni serĉis kafejon ĉie en la centro post la kunveno.

The original order sounds natural because it sets the time first: After the meeting...

Because serĉi already means to look for / to search for, and it takes a direct object directly.

So Esperanto says:

• serĉi kafejon = to look for a café

not something like serĉi por kafejo.

This is a common difference from English: some Esperanto verbs that match English phrasal verbs do not need an extra preposition.