Мне нравится доброта нашей новой соседки.

Russian uses нравиться differently from English to like.

Literally, мне нравится доброта... is closer to The kindness ... is pleasing to me.

So:

• мне = to me
• нравится = is pleasing / appeals
• доброта = the thing that is pleasing

That is why я is not used here.

Also:

• я люблю... means I love..., and it is usually stronger.
• я нравлюсь means I am liked / someone likes me, which is a completely different meaning.

Because with нравиться, the person who experiences the feeling is put in the dative.

So:

• мне = to me
• тебе = to you
• ему / ей = to him / her

Examples:

• Мне нравится музыка. = I like the music.
• Ей нравится этот фильм. = She likes this film.

This is one of the most important patterns to remember with нравиться.

The verb agrees with the thing being liked, not with the person in мне.

Here, the subject is доброта, and доброта is:

• singular
• feminine

In the present tense, нравиться uses:

• нравится for singular
• нравятся for plural

So:

• Мне нравится доброта... = I like the kindness...
• Мне нравятся книги. = I like books.

Even though мне means to me, it does not control the verb form.

Доброта is in the nominative case.

That is because it is the grammatical subject of the sentence — the thing that is pleasing.

Structure:

• Мне = to me
• нравится = is pleasing
• доброта = kindness

So доброта is the thing doing the grammatical work of pleasing.

Нашей новой соседки is in the genitive case.

It means of our new neighbor.

So:

• доброта соседки = the kindness of the neighbor
• доброта нашей новой соседки = the kindness of our new neighbor

The genitive is used here to show possession or relationship:

• whose kindness?
• our new neighbor's

That is why all three words are in genitive singular feminine:

• нашей
• новой
• соседки

Because both words are describing соседки, and adjectives/pronoun-adjectives in Russian must agree with the noun they modify.

Here соседки is:

• feminine
• singular
• genitive

So both modifiers must also be:

• feminine
• singular
• genitive

That gives:

• наша → нашей
• новая → новой
• соседка → соседки

This is a basic agreement pattern in Russian.

Yes. The base form соседка means female neighbor.

So:

• сосед = male neighbor
• соседка = female neighbor

In this sentence, соседки is the genitive singular form of соседка.

If the neighbor were male, you would say:

• Мне нравится доброта нашего нового соседа.

Notice how the modifiers would also change:

• нашего нового соседа = masculine genitive singular

Russian наш changes form to agree with the noun it describes.

It does not mean that the people who own the neighbor are feminine. It agrees with neighbor, not with we.

Base forms:

• наш = masculine
• наша = feminine
• наше = neuter
• наши = plural

But in this sentence, the word must be genitive singular feminine, because it describes соседки:

• нашей

So the change is grammatical agreement, not a change in meaning.

Yes. Russian word order is more flexible than English because the case endings show the relationships between words.

The neutral order here is:

• Мне нравится доброта нашей новой соседки.

But other orders are possible for emphasis, for example:

• Доброта нашей новой соседки мне нравится.
• Нашей новой соседки доброта мне нравится.

These all mean roughly the same thing, but the emphasis changes. The original sentence sounds natural and neutral.

Yes, but it means something different.

• Мне нравится доброта нашей новой соседки.
  = I like the kindness of our new neighbor.

• Мне нравится наша новая соседка.
  = I like our new neighbor.

The first sentence focuses specifically on one quality: kindness.
The second sentence is about the person in general.

• добрый is an adjective: kind
• доброта is a noun: kindness

So:

• добрая соседка = a kind neighbor
• доброта соседки = the neighbor's kindness

Russian often lets you express an idea either with:

1. an adjective describing the person, or
2. a noun naming the quality

This sentence uses the noun version.

A few words may be worth noticing:

• мне — pronounced roughly like mnye, with both consonants heard
• нравится — stress on the first syllable: НРА-вит-ся
• доброта — stress on the last syllable: добро-ТА
• соседки — stress on the second syllable: со-СЕД-ки

Also, -тся in нравится is pronounced like -ца in normal speech, so it sounds roughly like НРА-ви-ца.

That pronunciation is normal, even though the spelling stays -тся.