tikaku no sentou ha hurui keredo, yokusitu ga hirokute kanari kimotiii.

近く means nearby, the vicinity, or the area around here.
With の, it becomes a noun modifier: 近くの銭湯 = the bathhouse nearby / the neighborhood bathhouse.

Both are possible, but the nuance is a little different:

• 近くの銭湯: the bathhouse in this nearby area
• 近い銭湯: a bathhouse that is close

So 近くの sounds very natural when talking about a place in your area.

は marks the topic of the sentence.

So 近くの銭湯は means something like:

• As for the nearby bathhouse...
• The nearby bathhouse, ...

The rest of the sentence gives comments about that topic:

• it is old
• but the bathing area is spacious
• and it feels quite nice

This is a very common Japanese pattern: topic + comment.

They refer to different things:

• 銭湯 = a public bathhouse as a whole
• 浴室 = the bathing room / bathroom area inside it

So the sentence is not just repeating the same noun. It is saying:

• the bathhouse is old
• but the bathing room is spacious

That is why the sentence can sound balanced and natural.

けれど means but, although, or though.

Here it connects two contrasting ideas:

• 古い = it is old
• 浴室が広くてかなり気持ちいい = the bathing room is spacious and feels quite nice

So the sentence has this structure:

• It is old, but...
• Although it is old, ...

けれど is softer than a direct English but in some cases, and it is very common in everyday Japanese.

Because が marks what specifically has the property being described.

The topic of the whole sentence is already 近くの銭湯は.
Within that topic, the speaker then focuses on one part of it:

• 浴室が広い = the bathing room is spacious

So the structure is roughly:

• As for the nearby bathhouse, it is old, but its bathing room is spacious...

Using が here makes 浴室 the specific thing being described inside the larger topic.

Yes. 広くて is the て-form of the い-adjective 広い.

Formation:

• 広い
• remove い
• add くて
• 広くて

This form connects one description to another. Here it means something like:

• spacious, and...
• being spacious, ...

So:

• 浴室が広くてかなり気持ちいい means
• the bathing room is spacious and feels quite nice

It can suggest either simple connection or a reason, depending on context.

Here it can be understood as:

• the bathing room is spacious and quite pleasant
• or more naturally,
• the bathing room is spacious, so it feels quite nice

Japanese て-form often leaves the exact relationship slightly open. In this sentence, English speakers often feel a causal connection, but grammatically it is just a smooth connector.

かなり means quite, fairly, or considerably.

It modifies 気持ちいい:

• かなり気持ちいい = quite pleasant / feels really nice

It is stronger than just a mild a little, but not necessarily as emotional or direct as some stronger casual words. It sounds natural and conversational.

Here 気持ちいい means pleasant, comfortable, or feels good.

It does not mean something like a moral judgment or personality trait.
It describes the physical or sensory experience.

In this sentence, it suggests that:

• being in the bathing room feels good
• bathing there is pleasant
• the atmosphere is comfortable

So it is about the experience of the place.

Because Japanese often leaves obvious information unstated.

In English, you might expect something like:

• the bathing room is spacious, so bathing there feels quite nice
• the place feels quite pleasant

In Japanese, that extra explanation is often omitted if the meaning is clear from context.
Here, listeners naturally understand that the experience of using the bath or being in that bathing area feels good.

The grammar points more directly to the bathing room.

The sentence flow is:

• the nearby bathhouse is old
• but the bathing room is spacious
• and it feels quite nice

So the positive description is especially tied to 浴室.
However, in natural interpretation, that often extends to the overall experience of the bathhouse.

Yes:

• 近くの銭湯は
  As for the nearby bathhouse,

• 古いけれど、
  it is old, but

• 浴室が
  the bathing room

• 広くて
  is spacious, and / being spacious,

• かなり気持ちいい。
  feels quite nice.

A natural grammatical reading is:

• As for the nearby bathhouse, it is old, but the bathing room is spacious and quite pleasant.