Because of the $$$$ the cruise ships bring in, the waterfront and PIke Place Market are pretty safe.
The area known as Pioneer Square has always been divey but now is run by druggies and gangs. Shootings and assaults happen many times a week. It's sad because that area is also the home to the baseball, soccer and football teams and also had lots of night life.
I remember when Pioneer Square was called Skid Row back in the 60s. Then they spent a lot of money refurbishing it. Too bad.