Θα περιμένω μισή ώρα στην είσοδο.

Θα is the particle that gives the verb future meaning.
So:

• περιμένω = I wait / I am waiting
• θα περιμένω = I will wait

In Modern Greek, the future is normally formed with θα + verb.

It can do both, depending on context. Greek often uses περιμένω where English uses either wait or wait for.

For example:

• Περιμένω. = I’m waiting.
• Περιμένω τον φίλο μου. = I’m waiting for my friend.

In your sentence, there is no stated object, so it simply means I will wait.

Because Greek often expresses duration with just a time phrase by itself. So μισή ώρα can mean half an hour or for half an hour, depending on context.

That means:

• Θα περιμένω μισή ώρα = I will wait for half an hour

Greek can also use για in some contexts, but here μισή ώρα alone is very natural.

Because ώρα is a feminine noun, and μισός must agree with it.

Forms of μισός:

• μισός = masculine
• μισή = feminine
• μισό = neuter

So:

• μισή ώρα = half an hour

It is in the accusative here, but many feminine nouns ending in -α have the same form in the nominative and accusative singular.

So:

• η ώρα = nominative
• την ώρα = accusative

The article changes, but the noun itself looks the same.

Στην is the contracted form of σε την.

• σε = in, at, to
• την = the for a feminine noun in the accusative

So:

• σε την είσοδο becomes στην είσοδο

This contraction is normal in Modern Greek.

Because είσοδος is the dictionary form (nominative), but after σε Greek uses the accusative.

So:

• η είσοδος = the entrance
• στην είσοδο = at/to the entrance

This is a regular pattern: after σε, nouns go into the accusative.

The full form here is στην, and the final -ν is normally kept before a vowel. Since είσοδο begins with ε, στην είσοδο is the expected form.

You may hear the final -ν drop in other situations, especially before some consonants, but not here.

Usually yes. Greek uses the definite article much more often than English does. Στην είσοδο sounds natural because it refers to a specific entrance.

So even though English might sometimes say at entrance only in special contexts, Greek normally wants the article:

• στην είσοδο = at the entrance

Yes. Greek word order is more flexible than English word order, and changing it usually changes the emphasis, not the basic meaning.

For example:

• Θα περιμένω μισή ώρα στην είσοδο. = neutral
• Στην είσοδο θα περιμένω μισή ώρα. = emphasis on at the entrance
• Μισή ώρα θα περιμένω στην είσοδο. = emphasis on half an hour

The original sentence is a very natural, neutral way to say it.