There are no serious safety issues to speak of. The main danger you are likely to face in any Bulgarian city will come from the traffic. Cars often ignore pedestrian crossings and traffic lights, so be extra vigilant when crossing roads, although the problem is not as bad as in Sofia. In any city, be careful with bags, wallets and purses on crowded public transport and in crowded areas like markets. Flashing valuable jewelry about broadcast your wealth will invite trouble, as it will anywhere. Violent crime against tourists is extremely rare and most visitors encounter no problems whatsoever, but it's best to practice caution.