I'm trying to translate in English the part of address related to the name of the city. Which variant is correct?
1 - the city of Samara 2 - Samara
Just write Samara, for postal addresses.
Unless the official name of your city is actually "City of Samara" - e.g. in the US you have "Oklahoma City" which is the actual full name of the city.
Postal addresses have expected data in specific slots, e.g. for US postal addresses:
[Address Number] [Street Name] [Street Abbreviation]
[City] [State] [ZIP Code]
So it is usually known you mean a city already by where you put it in the address.