I would assume the Rainier Valley and parts of the Central, although the latter was being gentrified by the Capitol Hill crowd when I was living there. The areas around Pioneer Square are a little seedy, but I assume most of the crime there centers on fights over the last bottle of Thunderbird.
I have never seen a cop in the Pioneer Square area, but used to see cops in the Bowery, but that was in the days of cops walking a beat.