Budapest is a lively city. You can go for a concert any given day and some of the bars and clubs are packed even on Mondays, many patrons being foreigners living in Budapest. Budapest's nightlife is of course the liveliest from Thursday till Saturday. The streets in parts of the city with the greatest concentration of nightlife are never deserted and give an impression of safety.
Nevertheless you should never forget the golden rules of taking care of yourself and your belongings. Do not wander into dark side lanes at night, do not provoke drunken youngsters, do not show your money and expensive belongings in public and never carry your wallet in the back trousers' pocket or leave your handbag in a cloakroom.