In order to enter Turkey for touristic purposes as a US citizen, you need a visa which can be bought upon arrival. It costs $20:
American citizens traveling to Turkey on U.S. passports must obtain a visa. Currently, holders of all types of passports can purchase a 90-day sticker visa at the port of entry for $20 cash if they are traveling to Turkey as tourists.
As long as you do not exit the international terminal at the airport, you do not need a visa.
To travel to Italy, you do not need a visa. You can stay upto 90 days in Italy (Entire Schengen Zone) for touristic purposes as a US citizen.
U.S. citizens may enter Italy for up to 90 days for tourist or business purposes without a visa. All non-residents are required to complete a declaration of presence (dichiarazione di presenza).
For future references: This site is not Google. By typing "US citizen [country] visa" on google you can get the same results I got within seconds. Please do your research beforehand in the future.