Ο προορισμός μου είναι η Πάτρα, αλλά δεν βρήκα απευθείας πτήση.

Yes—προορισμός is a masculine noun in Greek, so it takes the masculine article ο in the nominative singular: ο προορισμός.

This is just grammatical gender, not real-world gender. Greek nouns are classified as masculine, feminine, or neuter, and you usually need to learn the noun together with its article.

In Greek, the unstressed possessive forms like μου, σου, του, της usually come after the noun:

• ο προορισμός μου = my destination
• το σπίτι μου = my house
• ο φίλος μου = my friend

So Greek often looks like the destination my when translated word-for-word.

Because after είναι (is), Greek uses the nominative case, not the accusative.

So:

• η Πάτρα = nominative
• την Πάτρα = accusative

In this sentence, η Πάτρα is the predicate noun after είναι, so nominative is correct.

Also, Greek often uses the definite article with place names and personal names, so η Πάτρα is perfectly normal.

That is just a difference between the Greek name and the conventional English name.

In Greek, the city is η Πάτρα.
In English, the usual form is Patras.

This is similar to other place-name differences, such as:

• Αθήνα → Athens
• Ρώμη → Rome

So the Greek word is not wrong or incomplete—it's simply the Greek name.

Βρήκα is the aorist form of βρίσκω (to find).

Here it means I found / I managed to find in the sense of a completed past action. With δεν, it becomes I didn’t find.

So:

• βρίσκω = I find / I am finding
• βρήκα = I found

If Greek wanted to stress an ongoing or repeated past situation, it would use the imperfect instead, for example δεν έβρισκα.

Because δεν is the normal negation word used before a finite verb in statements.

So:

• βρήκα = I found
• δεν βρήκα = I didn’t find

This is very standard Greek word order:

• Δεν ξέρω = I don’t know
• Δεν πήγα = I didn’t go
• Δεν βρήκα = I didn’t find

Greek often leaves out the indefinite article where English would use a or an.

So:

• δεν βρήκα απευθείας πτήση = I didn’t find a direct flight

You could say δεν βρήκα μια απευθείας πτήση, but the version without μια sounds very natural and neutral.

English requires a direct flight, but Greek does not always need the equivalent article.

Here απευθείας means direct and modifies πτήση, so in this sentence it functions like an adjective: a direct flight.

A useful thing to know is that απευθείας is indeclinable, which means its form does not change for gender, number, or case.

So you can have:

• απευθείας πτήση
• απευθείας πλοίο
• απευθείας δρομολόγια

The word stays απευθείας.

It can also function adverbially in other contexts:

• Πήγα απευθείας στο ξενοδοχείο = I went straight/directly to the hotel

It is the object, but for many feminine nouns in -η, the singular noun form looks the same in the nominative and accusative when there is no article.

So:

• η πτήση = the flight (nominative)
• την πτήση = the flight (accusative)

Notice that the article changes clearly, while the noun πτήση itself stays the same.

In your sentence, there is no article, so you just see πτήση.

Yes, Greek word order is more flexible than English word order.

For example, you could also say:

• Η Πάτρα είναι ο προορισμός μου, αλλά δεν βρήκα απευθείας πτήση.

That still means the same thing, but the emphasis changes slightly.
The original version, Ο προορισμός μου είναι η Πάτρα, sounds very natural and starts by focusing on my destination.

Greek often changes word order for emphasis, topic, or style rather than basic grammar.

Often yes, because both can mean but.

• αλλά is the more neutral, standard choice
• μα is common too, but can sound a little more conversational or stylistically different depending on context

In this sentence, αλλά is the safest and most straightforward option:

• Ο προορισμός μου είναι η Πάτρα, αλλά δεν βρήκα απευθείας πτήση.

Yes. Greek usually does not need the subject pronoun εγώ because the verb ending already shows the person.

So βρήκα already means I found, and with δεν:

• δεν βρήκα = I didn’t find

You would normally add εγώ only for emphasis or contrast:

• Εγώ δεν βρήκα απευθείας πτήση = I didn’t find a direct flight

So the sentence sounds natural without any separate word for I.