I learnt at school that "a pen to write" is incorrect and that you need to say "a pen to write with" because you don't write a pen but you write with a pen.
However, I found this sentence in a dictionary.
You don't unwind the bar but you unwind in the bar, don't you? Why don't you need to add the preposition, in, after "unwind" in the sentence above and make it like this?
It is not a universal rule.
In American English, for example, you will often see people say "I will write you".
Even the example given is wrong, because nobody would think it unnatural to say; "I need a pen to write".
There are many more examples.
e.g.
I use a stove to cook
Basically, any verb that can be use intransitively.
Context is all.
You have made the leap from a teaching aid
"a pen to write" is incorrect and that you need to say "a pen to write with"
I will assume what your teacher was saying, was
"I need a pen to write" is incorrect and that you need to say "I need a pen to write with"
Thus associating the pen with making marks on paper. This is one piece of information.
Fast forward to
You don't unwind the bar but you unwind in the bar, don't you?
When you look at the sentence you need to observe the context in which it is written.
The bar is a favorite of the locals to unwind after work.
your should now automatically separate that into two pieces of information
The bar is a favourite of the locals
Because two sentences have been combined to make this sentence we also know that it has elements that are common to both pieces of information "The Bar and The Locals"
(locals like) to unwind after work (in this place)
From the context we know they like this place because it is a favourite. We also know they are in the bar when they are relaxing, because it is the fact they are here that causes them to relax.
unwind verb (RELAX) CED (also wind down)
to relax and allow your mind to be free from worry after a period of work or some other activity that has made you worried:
It easy to comprehend the link between pen and writing but to comprehend the thought process of physically unwinding a bar takes a lot of comprehension.
The sentence you found is correct and natural, but you're right that it's ambiguous, and you could naively parse it to mean the locals like to unwind the bar after work. Lots of natural sentences in English can be parsed to have a meaning other than what was intended, so this alone isn't a problem. The question is how this sentence has the intended meaning, which becomes unambiguous when you add "in", as you have correctly done.
So let's take an unambiguous sentence with comparable underlying structure:
The park is a favourite place for people to meet.
In this sentence, even without any preposition, we understand that people meet at the park, not that people meet the park. If you wanted to though, you could naively parse "meet" as a transitive verb, with the park as the direct object, meaning "People commonly meet the park."
The bar is a favourite of the locals to unwind after work.
The same thing is happening in your example sentence, except "favourite" is understood to mean "favourite place", which is enough of a context clue to help the reader parse it as intended.
