Smoking is banned in Italy in all public places. This includes trains, buses, offices, hospitals, and waiting rooms, as well as restaurants, pubs, and discotheques (unless the latter have separate smoking rooms). If you want to smoke inside a restaurant, ask before booking; very few have smoking sections. Fines for breaking the law are exorbitant. Sit inside if the smoke in outdoor seating areas bothers you. Many restaurants are now equipped with air-conditioning.
It's always best to travel with your own trusted medications. Should you need medication while in Italy, you should speak with a physician to make sure it is the proper medicine and in case a prescription is necessary. Aspirin (l'aspirina) can be purchased at any pharmacy, as can over-the-counter medicines such as ibuprofen and Aleve. Other over-the-counter remedies, including cough syrup, antiseptic creams, and headache pills, are only sold in pharmacies.