Θέλω να βρω ένα καφέ που να έχει σκιά και αεράκι, ώστε να διαβάσουμε εκεί το απόγευμα.

Because Modern Greek normally does not use an infinitive the way English does. After verbs like θέλω (I want), Greek uses να + a finite verb form:

• Θέλω να βρω = I want to find
• literally: I want that I find

So να βρω is the standard Greek way to express what English does with to find.

Yes, καφέ can mean coffee, but it can also mean café in everyday Greek. Context tells you which one is meant.

In this sentence, ένα καφέ clearly means a café, because it is something that can have shade and a breeze and where people can read in the afternoon.

A useful note:

• καφέ in this sense is a colloquial, indeclinable noun.
• Many speakers would also say μια καφετέρια for a café.

So:

• ένα καφέ = a café
• έναν καφέ = a coffee very often, depending on context

This is a very common pattern in Greek.

που να έχει is used because the speaker is looking for a place with certain desired qualities, but has not identified it yet. It means something like:

• a café that has shade and a breeze
• or more literally/naturally in English: a café that would have shade and a breeze

So Greek often uses:

• θέλω / ψάχνω / προσπαθώ να βρω + noun + που να + verb

when talking about something wanted, searched for, or not yet found.

Compare:

• Θέλω να βρω ένα καφέ που να έχει σκιά.
  = I want to find a café that has / that would have shade.

• Ξέρω ένα καφέ που έχει σκιά.
  = I know a café that has shade.

The first is about a desired, not-yet-identified place. The second is about a real, known place.

Yes. In Modern Greek, the subjunctive is usually marked by particles like να, not by a completely different verb ending.

So in:

• που να έχει

the word να tells you the verb is in the subjunctive construction, even though έχει looks the same as the present indicative form.

This is very normal in Greek:

• έχει can appear in indicative contexts
• να έχει is the subjunctive construction

Because the speaker means these in a general, indefinite way:

• σκιά = shade
• αεράκι = a breeze / some breeze

They are qualities the café should have, not specific known things like the shade or the breeze.

So:

• να έχει σκιά και αεράκι = to have shade and a breeze

If you added articles, the meaning would become more specific or context-dependent.

Αεράκι is the diminutive of αέρας.

• αέρας = air / wind
• αεράκι = little breeze, light breeze

The diminutive often gives a softer, more pleasant feeling. In this sentence, αεράκι suggests a nice, refreshing breeze, which fits the idea of a comfortable café for reading.

So σκιά και αεράκι sounds very natural and pleasant: shade and a light breeze.

Here ώστε να introduces a purpose clause:

• ώστε να διαβάσουμε = so that we can read / in order to read

Yes, in many everyday contexts you could also use για να:

• ...ώστε να διαβάσουμε εκεί το απόγευμα
• ...για να διαβάσουμε εκεί το απόγευμα

Both are possible, but there is a slight nuance:

• για να is very common in everyday speech
• ώστε να can sound a bit more formal or slightly more polished/written

In this sentence, ώστε να is perfectly natural.

Because after ώστε να, Greek needs a subjunctive form, and here the speaker uses the aorist subjunctive:

• να διαβάσουμε

This does not mean past time. In this kind of sentence, the aorist subjunctive usually presents the action as a whole, as a single intended event:

• so that we can read there in the afternoon

If you said να διαβάζουμε, that would be the present subjunctive, which would emphasize duration, repetition, or an ongoing activity more strongly.

So:

• να διαβάσουμε = read, as a planned whole event
• να διαβάζουμε = be reading / read regularly or continuously

Yes, but εκεί is still very natural. It means there, referring back to the café:

• ώστε να διαβάσουμε εκεί = so that we can read there

Greek often keeps this kind of location word even when the place has just been mentioned, because it makes the sentence feel complete and explicit.

Without εκεί, the sentence would still be understandable, but εκεί neatly reinforces the idea of reading at that place.

Greek often uses the accusative as a time expression without a preposition.

So:

• το πρωί = in the morning
• το μεσημέρι = at noon / around midday
• το απόγευμα = in the afternoon
• το βράδυ = in the evening / at night

Here:

• εκεί το απόγευμα = there in the afternoon

This is a very common Greek structure.

Yes. Greek word order is fairly flexible, as long as the sentence remains clear.

For example, you could also hear:

• ...ώστε να διαβάσουμε το απόγευμα εκεί
• ...ώστε το απόγευμα να διαβάσουμε εκεί

The original order:

• ώστε να διαβάσουμε εκεί το απόγευμα

is completely natural. It presents the place first (there) and then the time (in the afternoon). Different word orders can slightly change emphasis, but not the basic meaning.

Definitely. It is a very useful pattern in Greek.

You will often hear it after expressions of wanting, searching, or needing:

• Ψάχνω σπίτι που να είναι κοντά στο κέντρο.
  = I’m looking for a house that is near the center.

• Θέλω κάποιον που να ξέρει ελληνικά.
  = I want someone who knows Greek.

• Χρειάζομαι ένα μέρος που να είναι ήσυχο.
  = I need a place that is quiet.

So in your sentence:

• ένα καφέ που να έχει σκιά και αεράκι

means a café that has / that would have shade and a breeze, in the sense of a desired kind of place.