Learn Hardcore Japanese: watasi no itiban no tanosimi ha natuyasumi desu.

First の: connects 私 to the rest → 私の一番の楽しみ = my biggest pleasure
Second の: connects 一番 to 楽しみ → 一番の楽しみ = number‑one pleasure / top enjoyment

So structurally it is:

(私の) (一番の) (楽しみ)

Each の belongs to a different connection, so two の are natural and necessary here.

Could I say 私の一番楽しみ without the second の?

Normally, no. 私の一番楽しみ sounds unnatural.

一番 by itself is a noun/adverb meaning number one / most, not an adjective. To use it to directly modify a noun like 楽しみ, you almost always need の:

一番の楽しみ ✅
一番楽しみ ❌ (unnatural in standard Japanese)

Think of 一番の楽しみ as the number‑one pleasure or the greatest pleasure. That の is playing the same role English uses word order or hyphenated phrases for, like number‑one hobby, top choice, etc.

Why not use は after 私 instead of の? For example, is 私は一番の楽しみは夏休みです correct?

私は一番の楽しみは夏休みです is not natural, because it has two は marking topics: 私は and 一番の楽しみは.

You normally choose one main topic with は. In the original sentence:

Topic: 私の一番の楽しみ
Comment: 夏休みです

So it is:

私の一番の楽しみは　→ as for my greatest pleasure,
夏休みです　　　　→ it is summer vacation.

If you really want to use 私は, you would typically change the structure:

私は夏休みが一番の楽しみです。
→ As for me, summer vacation is my greatest pleasure.

Here:

私は = topic (me)
夏休みが = subject (summer vacation)
一番の楽しみです = predicate (is the greatest pleasure)

So either:

私の一番の楽しみは夏休みです。 ✅
私は夏休みが一番の楽しみです。 ✅

But not 私は一番の楽しみは夏休みです。 ❌

Why is は used after 楽しみ instead of が? What would change with が?

は marks the topic, while が usually marks the subject (and often carries emphasis).

私の一番の楽しみは夏休みです。

私の一番の楽しみ = topic (what we are talking about)
夏休み = what that topic is
Meaning: As for my greatest pleasure, it is summer vacation.

If you say:

私の一番の楽しみが夏休みです。

then:

私の一番の楽しみ is the subject, and が highlights/contrasts it.
Natural in contexts like choosing among possibilities:
- (Talking about various pleasures)
  その中で、私の一番の楽しみが夏休みです。
  → Among those, the one that is my greatest pleasure is summer vacation.

In isolation, the は version sounds more neutral and textbook‑like. The が version tends to feel more focused or contrastive, depending on context.

Is 夏休みは私の一番の楽しみです also correct? How is the nuance different?

Yes, 夏休みは私の一番の楽しみです。 is perfectly correct.

夏休みは私の一番の楽しみです。
→ As for summer vacation, it is my greatest pleasure.
→ Focus: summer vacation
私の一番の楽しみは夏休みです。
→ As for my greatest pleasure, it is summer vacation.
→ Focus: my greatest pleasure

The information is the same, but the topic (the thing you present first) changes:

If the conversation is about my hobbies / pleasures, you naturally say the original sentence.
If the conversation is about summer vacation, you might choose 夏休みは私の一番の楽しみです。 instead.

Japanese lets you flip XはYです to YはXです to change what you highlight, without changing who‑is‑what.

What exactly does 楽しみ mean here? Is it fun, hobby, or something I look forward to?

楽しみ is a noun with a few related nuances:

Pleasure / enjoyment
- The thing that brings you joy.
Something to look forward to
- Anticipated enjoyment.
Sometimes: favorite thing / main joy in life

In 私の一番の楽しみは夏休みです, the nuance is:

The thing I look forward to most / my greatest pleasure is summer vacation.

So it is more than just fun in general; it is the most enjoyable thing, something you strongly anticipate.

Common patterns:

週末が楽しみです。
→ I am looking forward to the weekend.
将来の楽しみがたくさんあります。
→ I have many things to look forward to in the future.

What is the difference between 楽しみ and 楽しい?

They are related but different parts of speech:

楽しい
- i‑adjective
- Means fun / enjoyable / pleasant
- Modifies nouns directly:
  - 楽しいパーティー = a fun party
- Predicate:
  - パーティーは楽しいです。 = The party is fun.
楽しみ
- noun
- Means pleasure / enjoyment / something to look forward to
- Can appear as:
  - 楽しみです。 = (It is) a pleasure / I am looking forward to it.
  - 一番の楽しみ = greatest pleasure

There is also 楽しみな, which behaves like a na‑adjective:

楽しみなイベント = an event I am looking forward to

So:

楽しい = the feeling of fun or the quality of something (fun, enjoyable)
楽しみ = the thing that brings or will bring that fun (pleasure, anticipated joy)

Can I omit 私 and just say 一番の楽しみは夏休みです?

Yes, you can. In natural Japanese, pronouns like 私 are often omitted when obvious from context.

私の一番の楽しみは夏休みです。
→ Explicitly my greatest pleasure.
一番の楽しみは夏休みです。
→ The greatest pleasure is summer vacation.
→ In real conversation, listeners will usually understand this as my greatest pleasure if that is clear from the situation.

If you are answering a question like:

あなたの一番の楽しみは何ですか。
→ What is your biggest pleasure?

A natural answer is simply:

一番の楽しみは夏休みです。

No need to repeat 私 or 私の unless you want to emphasize it.

Why does the sentence end with です? Could I use だ instead?

です is the polite copula, used in the standard polite style (です・ます form). It functions like is / am / are in English but also adds politeness.

私の一番の楽しみは夏休みです。
→ Polite, natural with teachers, acquaintances, in writing, etc.

だ is the plain (casual) copula:

私の一番の楽しみは夏休みだ。
→ Casual, used with close friends, family, in informal writing, diaries, etc.

Main points:

Use です in most beginner‑level sentences, in class, and in polite conversation.
Use だ in casual speech when you are comfortable with plain forms and the social situation allows it.
Grammatically, both are correct; the difference is politeness and tone, not core meaning.

What does 一番 do here, and how else can it be used?

In this sentence, 一番 means number one / most and strengthens 楽しみ:

楽しみ = pleasure
一番の楽しみ = number‑one pleasure / greatest pleasure

Common ways 一番 is used:

Before adjectives (as an adverb)
- 一番大きい家 = the biggest house
- 一番楽しいゲーム = the most fun game
- 日本語が一番好きです。 = I like Japanese the most.
Before verbs (as an adverb)
- 日本で一番行きたい場所 = the place I most want to visit in Japan
With の + noun (like in your sentence)
- 一番の友達 = number‑one friend / best friend
- 一番の問題 = biggest problem
- 一番の楽しみ = greatest pleasure

So 一番 is a very common word meaning most / number one, and の lets it directly modify a noun.

How do you pronounce the whole sentence, and is there anything tricky about the particles?

The sentence is pronounced:

わたしのいちばんのたのしみはなつやすみです。

Word by word:

私 → わたし (watashi)
の → no
一番 → いちばん (ichiban)
の → no
楽しみ → たのしみ (tanoshimi)
は → わ (wa) ← particle は is pronounced wa
夏休み → なつやすみ (natsuyasumi)
です → です (desu; often pronounced a bit like dess)

The main tricky point for learners is that when は is a particle (topic marker), it is written は but pronounced わ. The same goes for へ (pronounced え) and を (pronounced お), but they do not appear in this sentence.

Why are there spaces between the words in 私　の　一番　の　楽しみ　は　夏休み　です? I thought Japanese usually has no spaces.

You are right: normal Japanese writing does not use spaces between words.

The version with spaces:

私　の　一番　の　楽しみ　は　夏休み　です。

is a teaching aid. Textbooks and teachers often add spaces when presenting new sentences to:

Show word boundaries more clearly.
Help learners see where each grammar piece (like の, は, です) starts and ends.
Make it easier to match each part with a gloss or translation.

In real Japanese writing aimed at native speakers, you would normally see:

私の一番の楽しみは夏休みです。 (no spaces)

So the spaces are for your learning convenience, not part of standard Japanese orthography.