Awesome English Gabriele!

I have some minor recommendations that might improve it but some of them depend on the nature of your relationship with Mike and whether he uses British or American English. I must stress that these suggestions are very minor and some might think I'm being very picky indeed. There would be little doubt about the meaning of what you wrote. However, from the quality of your writing I assume that you seek perfection and hope you find the "correction" useful.

Letter To a Friend

A friend asked me by email what it would be better visit in my city and to recommend some interesting places:

Hi Mike,
I’m very glad to read that you will be able to visit my Region next month.
Unfortunately, you don’t have many days to spend but I can give you some useful advice.
First of all you must visit our Egiptyan Egyptian Museum in Turin because it was recently restructured and it is one of the most important in the world. Secondly you can visit King’s royal(1) castles and residences: for examples:(7) Palazzo Reale, Palazzo Madama, Stupinigi, Venaria and the art gallery behind the main Cchurch of in the city (the “Duomo"). There are a lot of beautiful churches in Turin and in nearby villages(2) Turin. One of the most important churches typical of medioeval with typical medieval architecture is the “Sacra di San Michele” which is placed situated on a mountain 20 kilometers kilometres(3) from Turin, an abbey that you can visit every day.
Don’t miss the Cinema mMuseum and the panoramic lift of “Mole Antonelliana”. and t(4)Take a stroll in the city: view the streets, come into the shops and taste our typical food in the restaurants.
I look forward to hearing from you in the next weeks near future(5) so we can arrange a date and spend a pleasant dinner together(6)

Best wishes
Gabriele

(1) I assume you meant that the castles and residences were built for kings so they have the quality of being royal. King's implies posession but I presume the kings in question are dead.

(2) Nothing technically wrong with "near Turin" but since you have already used the word in the sentence it is stylistically better not to repeat it. 

(3) Kilometres is the British spelling, kilometers is the US spelling. We also pronounce them differently sometimes. 

(4) Too many "ands". 

(5) Or coming weeks.

(6) Because you followed "arrange a date" with "and" this might read like you mean a romantic meeting. If that's not what you mean then you might use something like "arrange a date to …" instead. Also whilst the meaning of "… spend a pleasant dinner together" is clear it might be better to say "… share a pleasant dinner.", "… enjoy a pleasant dinner together." or "... spend time enjoying a pleasant dinner together.". We speak of spending time with someone else. You can't spend a meal because they aren't money - at least not where I live ;). 

(7) A colon should only be used to introduce something that is an explanation or elaboration of what precedes it. What precedes the colon must normally be a complete sentence. In your sentence, where you are providing a list of royal castles and residences, the colon would take the place of the words "for example". Unless the art gallery is royal i.e. it is part of the same list then you should move this to another sentence and insert the word "and" before the last item of the list.

So " … royal castles and residences: Palazzo Reale, Palazzo Madama, Stupinigi and Venaria." in British English. However, in American English, the list is punctuated with commas slightly differently: " … royal castles and residences: Palazzo Reale, Palazzo Madama, Stupinigi, and Venaria.". Note the comma before the and preceding the last item in the list.

These differences between American and British English are normally unimportant when writing to friends (unless they are pedantic ones). It is only when writing formally that they matter.