In Lima ring 105. In Lima and some of the larger cities there is a sort of local police called "Serenazgo": you may ask for help but they have no tourist oriented services.
Be aware of your surroundings and try to avoid unlit or unpopulated areas especially at night. There is a lot of petty crime that can turn violent. Avoid groups of male youngsters since there are many small gangs trying to rob passers-by. If you witness a robbery. be very careful before intervening, since robbers may be armed and are quite prone to shooting if they feel threatened.
Armed robberies of tourists are fairly common.
A dirty old backpack with valuable contents is safer than a new one with old clothes in it. It's often good not to look too rich.
Some travelers don't use wallets, but keep the bills and coins directly in their pocket. Let's say some little bills on the left side and the rest on the right side. Thus, the pickpocket's job gets much harder.
Don't walk around with debit or credit cards in your pocket. Leave them in a safe place when you do not directly need them, because tourists have been kidnapped and forced to take out money each day for a period of a few days.
If you want to take large amounts of cash out with you, a neck wallet is always a good idea - you can hide it under your shirt.
Watch out for false bills. Every bank has posters that explain what to check when getting higher valued bills. The only security element that has not been falsified is the bichrome 10,20,50,100 or 200 now also used on US$ bills. Don't be shy about checking any bills you receive. Most Peruvians do so, too. You may get false bills even at upscale places or (quite unusually, but it's been known to happen) banks, so check there too.
Ignore any requests to carry luggage or packages for strangers. There could be illegal items or drugs in there, and you are the one who'll be caught with them and have the problems afterwards.
Small quantities of drugs for personal use or possession (up to 2 g for powdered cocaine or 8 g for marijuana) are permitted by law (Section 299 of the Penal Code of Peru) PROVIDED THAT the user is in possession of only ONE type of drug. However, if you purchase drugs, know your source. It may be inadvisable to buy from strangers or street dealers.
REGARDING MARIJUANA in Peru: Possession for personal consumption in the max amount of 8 g is legal according to the Peruvian Penal Code article 299. What is considered illegal is the trafficking part, that is: buying, selling or having more than 8 g. So be careful who you buy from and do not buy more than 8 g per person.
When taking a taxi, take a quick look in the back seat and in the trunk, to make sure there is nobody hiding there. There've been reports of armed robberies/kidnappings taking place in taxis. Afterwards, tourists are blindfolded and driven outside the city and left behind by the highway.
At the border crossing from Ecuador (Huaquillas) to Peru people have tried to steal passports by acting like plain clothed police officers. They give you another form to fill in which is fake. This has taken place although police and customs personnel have been next to them.
When traveling on buses, it is recommended to keep your backpack under your seat with the strap hooked around your leg.
Tourist police are dressed in white shirts, instead of the usual green ones, and normally speak English and are quite helpful to tourists. The common police officer does not speak other language but Spanish but normally will try to help. DO NOT get in an argument with police, since they may forget about your needs and feel insulted.
Dealing with the police can take a lot of time. In order to get a copy of a police report you need to go to a Banco de la Nación and pay 3 soles. Without this the police won't give you a copy, and obviously you can only arrange this during working days.