Kind of a rock and a hard place situation.
Given the quality of the New York City voters, and their limited reasoning ability, Bloomberg is the absolute best you can hope for, unfortunately.
Giuliani was elected because things were so bad under the Democrats that enough people finally saw that things couldn't continue that way. Now that Giuliani cleaned things up quite a bit, and Bloomberg has basically maintained that, many people tend to want to slip back to the hare-brained liberal policies that brought them to grief earlier. They have forgotten how bad the results of those programs were.
People get the government they deserve, and if NYC voters elect somebody like Ferrer or Gifford, then they'll deserve the terrible results they get. Then you'll see renewed support for secession from the city by Staten Island, which only cooled down when Giuliani was elected. It was Staten Island that provided Giuliani with his margin of victory in 1993.