Learn Hardcore Indonesian: Hari ini saya pergi ke klinik kecil dekat rumah. - Today I go to a small clinic near the house.

Putting Hari ini at the beginning emphasizes “today” a bit more.
Putting hari ini at the end feels a bit more neutral in casual speech.
Grammatically, both are fine and very common.

How do I know if this means “I went” or “I am going” or “I will go” today?

Indonesian verbs don’t change form for tense, so pergi can mean go / went / am going / will go.
Hari ini only tells you the time frame (today), not whether it’s past, present, or future.
Context usually makes it clear:

Tadi pagi, hari ini saya pergi ke klinik kecil dekat rumah. → clearly past (this morning, today I went…)
Nanti siang, hari ini saya pergi ke klinik kecil dekat rumah. → clearly future (later at noon, today I will go…)

If you really want to mark tense, you can add adverbs like:

sudah / tadi → past
sedang → in the middle of doing (present, ongoing)
akan / nanti → future

Why do we need ke in pergi ke klinik kecil? Is pergi klinik kecil wrong?

You need ke after pergi, because ke means “to (a place)”.
Pergi almost always takes ke when followed by a destination:

Saya pergi ke sekolah. (I go to school.)
Dia pergi ke kantor. (He/She goes to the office.)

Pergi klinik kecil is ungrammatical in standard Indonesian.
Think of pergi ke as a unit: go to → pergi ke.

Why is it klinik kecil and not kecil klinik, even though in English we say “small clinic”?

In Indonesian, adjectives usually come after the noun:

klinik kecil = small clinic
rumah besar = big house
mobil baru = new car

So klinik (clinic) comes first, and kecil (small) describes it.
Putting the adjective before the noun (kecil klinik) is incorrect.

Does klinik kecil mean “a small clinic” or “the small clinic”?

Indonesian normally doesn’t mark a/the directly.
Klinik kecil by itself can mean either “a small clinic” or “the small clinic”, depending on context.
If you need to be specific, you can add words:

klinik kecil itu → that small clinic / the small clinic
sebuah klinik kecil → a small clinic (more clearly “one small clinic”)

Is dekat rumah complete and natural, or should it be dekat dengan rumah or di dekat rumah?

All of these are possible, but there are small differences in style:

dekat rumah – very common in everyday speech, short and natural.
dekat dengan rumah – a bit more explicit/clear, slightly more formal.
di dekat rumah – emphasizes the location “at near the house”; also very natural.

So you can say:

Hari ini saya pergi ke klinik kecil dekat rumah.
Hari ini saya pergi ke klinik kecil di dekat rumah.

Both are fine and common.

Can I drop saya and just say Hari ini pergi ke klinik kecil dekat rumah?

You can drop saya, but only if the subject is already clear from context.
In conversation, if it’s obvious that you’re talking about yourself, people may omit saya:

A: Kamu ke mana? (Where are you going?)
B: Hari ini pergi ke klinik kecil dekat rumah.

In a standalone sentence with no context, it’s safer and clearer to include saya.

What’s the difference between saya and aku here? Could I say Hari ini aku pergi ke klinik kecil dekat rumah?

Yes, you can say:

Hari ini saya pergi ke klinik kecil dekat rumah.
Hari ini aku pergi ke klinik kecil dekat rumah.

Saya is more formal and neutral, used in polite or formal situations, with strangers, in writing, etc.
Aku is more informal and intimate, used with friends, family, or in casual contexts.
Grammar stays the same; only the level of formality changes.

Is klinik different from rumah sakit?

Yes:

klinik = clinic (usually smaller, for lighter/less serious cases or specific specialties)
rumah sakit = hospital (larger facility, for more serious treatment, inpatient care, etc.)

So klinik kecil dekat rumah suggests a small local clinic near your house, not a full hospital.

Could I move dekat rumah earlier, like Hari ini saya pergi ke klinik dekat rumah yang kecil?

That version is grammatical but changes the structure and sounds less natural for the simple idea.

klinik kecil dekat rumah = a small clinic near (my/the) house.
klinik dekat rumah yang kecil = a clinic near the house that is small (now rumah is what’s being described as small).

If you want to keep the clinic as “small”, it’s more natural to keep kecil right after klinik:
Hari ini saya pergi ke klinik kecil di dekat rumah.

How would I say “the small clinic near my house” more explicitly?

You can make “my house” explicit:

klinik kecil dekat rumah saya
klinik kecil di dekat rumah saya

If it’s a specific clinic that both speaker and listener know, you can also add itu:

klinik kecil di dekat rumah saya itu = that small clinic near my house / the small clinic near my house.

What level of formality does this sentence have? Is it okay in polite conversation?

Hari ini saya pergi ke klinik kecil dekat rumah. is neutral and acceptable in polite conversation.
Using saya and not using slang keeps it standard and polite.
You could say this to a coworker, a teacher, or a doctor without sounding too casual or too stiff.