Yes, Zagreb is safe for tourists, it is safe to walk at night, it is safe to talk to locals. However, lately there are pick pocket gangs that aim to rob tourists and locals off. Be aware of that, always have your bag up on your belly front, or hidden under the jacket. Ladies handbags and rucksacks are to be worn up front, never on tha back.
Pick pocketers usually operate at main tourists sights, such as Zagreb Cathedral, Stone Gate Zagreb, St. Mark’s Church, Lotrscak Tower, places where there are crowds of people. Especially be very carefull when going down the stairs from Upper Town, using Zakmardijeve Stube
Young criminals usually sit on the wall and wait for their chance to rob you off.
When using ATM, always hide your PIN number.