"There is a park in the middle of the city."
Translation:C'è un parco nel mezzo della città.
I consider centro to have a slightly different connotation ... I am not saying that centro does not mean middle; however, consider the following:
When entering a city one sees a white sign in black print with a circle that points to IL CENTRO. This means the business district, which, as towns develop, may not always be in the middle. There are also brown signs with white printing saying: CENTRO STORICO = historical center
Therefore, for middle I would use mezzo not centro
"Although i have to say that noone says: c'è un parco nel mezzo della città. It is correct, but not used." How would you say it? If the word centro is used, I would take it to mean in the business district. centrale could be used. I may be the only one who thinks of centro this way, but in all my years driving in Italy (10), this has been my experience.
The fact is that the spoken italian is different from the signals' ones. Centro is a really used word: sto andando in centro (im going to the centre) or centro città (city centre) . Centro is only the part of the city where there are a lot of people, doing shopping, working, and so on, in the spoken italian. What ypu are saying is also correct but it is a technical language. Anyway i want to add that nel mezzo della città is antiquated, in mezzo alla città means in the city, maybe not in the city centre, but simply not in theoutside of the city. While in the centre means in the most trafficated zone.
I am not sure if I understood your question, but I'll try to answer: no, "nel" is not strictly connected to "della", just like "in" is not strictly connected with "alla". Simply the sentence "in mezzo della città" doesn't sound right. It's about harmony between the elements of the sentence. In italian, is really difficult to make clear rules, because there are much more exceptions than rules. I hope I helped you.