Being home to over 2,000,000 people, Lisbon is one of Europe's safest cities. However caution should be given when in Rossio Metro station and square, where many questionable characters hang out and offer miscellaneous drugs and substances to tourists at all times of the day (they may literally try to hand these supposed drugs to you as you walk by). The same characters operate in groups and usually wander up the main pedestrianised shopping streets in between Rossio Square and Terreiro do Paço square. Do not linger too long in Rossio as there are also many homeless people that keep their eyes peeled on the tourists. 

When on the Metro it is quite common to come across blind beggars as they ride the train from end to end. They typically do not cover their eyes and although harmless, it can be a confronting experience when they walk by you asking for money. Just be prepared for this.

To avoid being pickpocketed, men should carry wallets in their front pockets and women should hold their bags by their bodies, not their straps, while walking or shopping.  Women should also keep a close eye on their bags while eating in restaurants or using public transport.  Hotel safes should be put to use to store valuables and money, and a photocopy, not the original, of your passport should accompany you when you go out.  Leave the original in the safe.  Carry only small amounts of cash and avoid wearing expensive jewelry and engaging in behaviors that thieves may notice, such as overtipping. 

 Hospital da Luz is a really good private hospital, and many internationals go there too.