Varna is the third largest city in Bulgaria, with a population of 334,781 inhabitants, and is considered very safe - so you can enjoy walking around even after dark. Obvious caution is advised like sticking to well lit and frequented public areas.
By far the most common crimes are pick pocketing, car theft and burglaries. Burglaries tend to happen at night and usually the thieves are after cash, smartphones and laptops possibly jewellery. There are hardly any incidents of violent crimes towards foreigners, although it is advisable to avoid any form of confrontation especially when alchohol has been consumed.