Для нас эта конференция — хороший повод встретиться с друзьями из других городов.

Для нас literally means “for us” or “as far as we are concerned.”

• для always takes the genitive case.
  
  • мы (we) → нас in genitive.
  • So для нас = for us (genitive), not для мы or для нам.

Compare:

• для нас это важно – this is important for us.
• нам важно – it is important to us (using dative, more like “to us it is important”).

In your sentence, для нас sets the perspective: from our point of view / for us, this conference...

Yes. In Russian, in the present tense, the verb “to be” (быть) is usually omitted, and a dash often marks the connection:

• эта конференция — хороший повод
  ≈ this conference is a good reason/occasion.

You could also say:

• Эта конференция является хорошим поводом. (more formal, with an explicit verb)
• Эта конференция — хороший повод. (normal, neutral style)

The dash shows the link subject → predicate when both parts are nouns/noun phrases in the nominative:
эта конференция (subject) — хороший повод (predicate).

Эта конференция is in the nominative case, because it’s the subject of the sentence.

• эта конференция – nominative (who/what? this conference)
• эту конференцию – accusative (whom/what? this conference – as an object)

In your sentence, конференция is not being acted upon; it is the thing being described:
эта конференция — хороший повод → this conference is a good occasion.
So the subject has to be in nominative: эта конференция, not эту конференцию.

Хороший повод is in the nominative case, because it is the predicative part of “X is Y”:

• эта конференция — хороший повод
  Subject (nominative) — Predicate (also nominative).

In Russian, after the implied “to be” in such constructions, the predicate noun is usually in the nominative, not in another case.

Also note gender agreement:

• повод is masculine, so we use хороший (masculine form), not хорошая or хорошее:
  • хороший повод (m.)
  • хорошая причина (f.)
  • хорошее событие (n.)

Both can be translated as reason, but there is a nuance:

• повод – a pretext / occasion / handy reason to do something.
  Often something neutral or convenient that gives you an excuse or opportunity.
• причина – a real cause, the underlying reason why something happens or exists.

In this sentence:

• хороший повод встретиться → a good occasion/opportunity to meet. The conference itself may not be the deep “cause”; it just conveniently gathers people so you can meet.

If you said:

• Эта конференция — причина наших встреч.
  That would sound like the conference is the actual causal reason meetings happen at all, which is a bit different.

Встретиться is the perfective reflexive infinitive and here means “to meet (up)”, usually mutually and one time.

Compare:

• встретиться с друзьями – to meet (up) with friends (once, as an event).
• встречаться с друзьями – to meet with friends regularly / to hang out (on a regular basis) (imperfective, repeated action).
• встретить друзей – to meet / run into / greet friends (non‑reflexive, focuses more on you encountering them, not necessarily mutual arrangement).

Because the conference is a single event and a single occasion to meet, встретиться (perfective, one‑off) is the natural choice.

The verb встретиться in the meaning “to meet (with someone)” typically takes с + instrumental case:

• встретиться с кем? – to meet with whom?
  
  • с другом (with a friend)
  • с друзьями (with friends)

So:

• с друзьями is instrumental plural of друг.

This is a pattern to remember:

• говорить с кем – to speak with someone
• спорить с кем – to argue with someone
• встретиться с кем – to meet with someone

Друзьями is the instrumental plural of друг (friend).

Full main forms of друг:

• Nom. sg.: друг – a friend
• Gen. sg.: друга
• Dat. sg.: другу
• Acc. sg.: друга
• Instr. sg.: другом
• Prep. sg.: о друге

Plural:

• Nom. pl.: друзья – friends
• Gen. pl.: друзей
• Dat. pl.: друзьям
• Acc. pl.: друзей
• Instr. pl.: друзьями ← used in the sentence
• Prep. pl.: о друзьях

So с друзьями = with friends (instrumental plural).

The preposition из (“from, out of”) requires the genitive case.

• город (city) → городов in genitive plural.
• The adjective другие must agree with городов in case (genitive) and number (plural), so it becomes других.

So we get:

• из других городов – from other cities
  
  • из
    • других (gen. pl.) + городов (gen. pl.)

Forms to compare:

• Nominative plural: другие города – other cities (as subject/object)
• Genitive plural: других городов – of/from other cities (after из, нет, etc.)

Both из and от can translate as from, but they’re used in different contexts:

• из – literally “out of, from inside” some place or group:

  • из Москвы – from Moscow
  • из России – from Russia
  • из других городов – from other cities

• от – more like “from (a person, source, direction towards you)”:

  • письмо от друга – a letter from a friend
  • подарок от родителей – a present from (your) parents
  • убежать от врага – to run away from an enemy

Here we talk about people coming from cities (as locations), so из других городов is correct, not от других городов.

Yes, you can say:

• Эта конференция для нас — хороший повод встретиться с друзьями из других городов.

The basic meaning stays the same, but emphasis shifts:

• Для нас эта конференция — хороший повод...
  Emphasis: for us this conference is a good occasion (maybe for others it isn’t).
• Эта конференция для нас — хороший повод...
  Emphasis: this conference, for us, is a good occasion (slightly more focus on the conference itself).

Both are natural; Russian word order is flexible and often used to highlight what the speaker finds most important.