Good advice—last time I was there (business—urgent—could not pick decent hotels) I was in a sketchy area.
After I left I wrote a lengthy email to the hotel explaining that they needed to tighten up their security since street people were gaining access to the lobby late at night.
They were not pleased with my email—I bet they got a lot more like it....
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.