kazoku to issyo ni mita hanabi ha natu no ii omoide desu.

A helpful breakdown is:

• 家族と一緒に = together with (my) family
• 見た花火 = the fireworks (I) saw
• は = topic marker
• 夏のいい思い出です = are a good summer memory / is a nice summer memory

A very literal order is:

As for the fireworks I saw together with my family, they are a nice summer memory of summer.

More natural English usually reshapes it a bit.

Because Japanese puts modifying clauses before the noun.

So:

• 見た花火 = the fireworks that I saw

This is like a relative clause in English, but Japanese does not use words like that, which, or who here.

This is a very common question.

In a normal sentence, you would say:

• 花火を見た = I saw fireworks

But in a relative clause, the noun being modified moves outside the clause:

• 見た花火 = the fireworks that I saw

Japanese does not leave the original particle on the noun in this structure. So 花火 is understood as the object of 見た, even though を is not shown.

• 家族と = with family
• 一緒に = together

So 家族と一緒に means together with my family.

Why both?

• と marks the companion: with family
• 一緒に adds the idea of together
• に makes 一緒 function adverbially, so it modifies the verb 見た

You could sometimes just say 家族と見た, but 一緒に emphasizes the shared experience more clearly.

一緒 is often treated as a noun-like or na-adjective type word.

Common patterns are:

• 一緒に行く = go together
• 一緒だ = be together / be the same
• 一緒の時間 = time together

In this sentence, 一緒に is being used adverbially to describe how the fireworks were seen.

Because the whole noun phrase 見た花火 is the topic of the sentence.

So the structure is:

• [家族と一緒に見た花火] は ...

This means the sentence is making a comment about the fireworks I saw with my family.

The は does not attach to 見た because は normally marks a noun phrase, not a verb.

• 夏 = summer
• の = links nouns
• いい = good / nice
• 思い出 = memory

So 夏のいい思い出 means:

• a nice summer memory
• or a good memory of summer

Here, の connects 夏 and 思い出. It is often possessive in English, but more broadly it just links nouns.

いい is the usual everyday form of 良い／よい, meaning good.

So:

• いい思い出 = a nice memory
• よい思い出 = also correct, but a bit more formal or literary in tone

A useful thing to remember is that this adjective behaves irregularly in some forms:

• いい → よかった in the past
  not いかった

Because the two parts are talking about different things:

• 見た = the act of seeing happened in the past
• です = the sentence is stating, now, that it is a good memory

So the idea is:

The fireworks I saw with my family are now a nice summer memory.

This combination is completely normal in Japanese.

Japanese nouns usually do not show singular vs. plural the way English does.

So 花火 can mean:

• a firework
• fireworks
• a fireworks display

In this sentence, it most naturally refers to fireworks as an event or display.

Japanese often leaves out things that are clear from context.

So:

• 家族 often naturally means my family in a sentence about your own experience
• the subject I is also omitted because it is obvious from the context of 見た

English usually requires these words, but Japanese often does not.

Yes. That is a very natural English translation.

Japanese is phrased more like:

The fireworks I saw with my family are a nice summer memory.

But English often prefers to turn that into an event:

Seeing fireworks with my family was a nice summer memory.

So even if the Japanese grammar centers on 花火, the most natural English may center on the experience instead.