tosyokan no tikaku no kafe ha suiyou ga teikyuubi rasii node, asita ha betu no mise ni ikimasu.

A good way to break it down is:

• 図書館 = library
• 図書館の近く = the area near the library
• 図書館の近くのカフェ = the cafe near the library

So the の is chaining nouns together.

You can think of it as:

• library + near + cafe
• more naturally: the cafe near the library

In Japanese, 近く is a noun here, meaning vicinity / nearby area, so 図書館の近く literally means the library's vicinity or the area near the library.

Because の does several very common jobs, especially linking nouns.

In this sentence:

• 図書館の近く = near the library
• 近くのカフェ = cafe in that nearby area
• 別の店 = another/different shop

So の is not always possession like John's book. It can also mean things like:

• location relation: near the library
• description: another shop
• category/specification

It is one of the most flexible particles in Japanese.

は marks the topic: what the sentence is about.

So 図書館の近くのカフェは means:

• As for the cafe near the library...
• The cafe near the library...

The sentence is then making a statement about that cafe: it seems Wednesday is its regular closing day.

This is very natural in Japanese. Even when English would just use the cafe, Japanese often uses は to set it up as the topic.

This is a very common question.

水曜が定休日 is natural because が identifies what the regular closing day is.

It is like saying:

• Wednesday is the day that is the regular holiday/closing day

With words like 定休日, 誕生日, 問題, and similar noun predicates, が often marks the item being identified.

So:

• 水曜が定休日です = Wednesday is the regular closing day.

If you said 水曜は定休日です, it can also be possible in some contexts, but it feels more contrastive, like:

• As for Wednesday, it is a regular closing day
  maybe implying comparison with other days

In this sentence, が is the more straightforward choice.

定休日 means a regularly scheduled day off / regular closing day for a business.

So it is not just closed this one time. It means the shop normally closes on that day every week.

For example:

• 月曜が定休日です = Monday is our regular closing day.

This is a set business word, often seen on signs, websites, and store information.

Here, らしい means something like:

• apparently
• it seems
• I heard that

So 水曜が定休日らしい means:

• Apparently Wednesday is their regular closing day
• It seems Wednesday is their regular closing day

This shows the speaker is not presenting the information as direct, certain personal knowledge. Maybe they heard it from someone, saw it online, or are otherwise not 100% asserting it from direct confirmation.

They are similar, but not identical.

In this sentence, らしい gives a sense of:

• from what I've heard / from available information
• apparently

そうだ can also report hearsay:

• 水曜が定休日だそうです = I heard Wednesday is their regular closing day.

A rough difference is:

• そうだ often sounds more directly reported: I heard that...
• らしい often sounds like it seems / apparently, based on hearsay or clues

In many everyday cases, both could work, but the nuance is a little different.

Both can mean because / since, but ので usually sounds a bit softer and more explanatory.

• A ので、B = because A, B
• A から、B = because A, B

In this sentence:

• 水曜が定休日らしいので、明日は別の店に行きます。
• Because it seems Wednesday is their regular closing day, we'll go to a different shop tomorrow.

Using ので fits well because the speaker is calmly giving a reason for the decision.

Very roughly:

• ので = explanatory, softer, more neutral/polite
• から = more direct, sometimes more assertive

明日は marks tomorrow as the topic or as a contrastive time frame.

So it gives a feeling like:

• As for tomorrow, we'll go to a different shop
• Tomorrow, at least, we'll go to a different shop

The は can lightly contrast tomorrow with other times. For example, maybe today is different, but tomorrow the plan changes.

If you said just 明日別の店に行きます, that is also understandable, but 明日は sounds very natural when setting tomorrow as the time being discussed.

別の means:

• another
• a different

So 別の店 means:

• another shop
• a different cafe/store

It implies not this one. Since the cafe near the library is apparently closed on Wednesday, the speaker plans to go somewhere else.

Yes, both に and へ can be used with 行く.

• 店に行きます
• 店へ行きます

Both mean go to the shop.

The difference is small:

• に strongly marks the destination
• へ emphasizes the direction toward it a little more

In everyday speech, に is extremely common, and it sounds perfectly natural here.

Yes.

• 水曜 = Wednesday
• 水曜日 = Wednesday

水曜 is just a shorter form, and it is very common in everyday Japanese.

So these are both natural:

• 水曜が定休日らしい
• 水曜日が定休日らしい

The shorter form often sounds a bit more casual or compact.

Japanese often leaves out subjects when they are understood from context.

So 別の店に行きます could mean:

• I will go to another shop
• we will go to another shop
• sometimes even someone will go to another shop

The meaning depends on the situation.

In this sentence, the implied subject is whatever the context already makes clear, often I or we. Japanese does this constantly, and it is completely normal.

The comma after ので helps separate the reason from the main action:

• 水曜が定休日らしいので、
• 明日は別の店に行きます。

So it marks:

• reason first
• then the result/plan

Japanese punctuation is somewhat flexible, and commas are often used to make a sentence easier to read. The sentence would still be understandable without it, but the comma makes the structure clearer.

Usually, no.

Normal Japanese writing would be:

図書館の近くのカフェは水曜が定休日らしいので、明日は別の店に行きます。

Spaces are often added only in teaching materials to help learners see the word boundaries. So the spaced version is learner-friendly, but not standard everyday writing.