Crime in Long Beach is generally down over the past few years, which also mirrors the trend for Los Angeles County. Of course there is still crime, and other nuisance issues in all neighborhoods. I suggest three things: (a) drive the neighborhoods you are interested in at various times of the day, evening and night; (b) speak with people who live and work in the neighborhood; (c) visit the local police station and ask them how the neighborhood you are interested in stacks up against other neighborhoods in the city in terms of violent crime and burglaries, breaking and entering, theft, etc.
Good luck, and please remember that there is some crime in every area no matter where you go.
Realtor and Loan Officer