The same question dawned on the New York Times, which offers the answer: Public Advocate Betsy Gotbaum. As the Times explains, the city rules for special elections are a bit murky, so it's unclear whether she would serve out the rest of Bloomberg's term, which ends in January 2010.
Gotbaum, 68, is a veteran of city government who keeps a low profile. She would be a notable mayor for a couple of reasons beyond, you know, running a city of 8 million people. She'd be New York City's first Democratic mayor in 15 years and the only woman nationwide in charge of a city of a million or more people, unless a woman wins elsewhere between now and then (Dallas' Laura Miller is leaving office).
Her tenure also might prompt someone to write, "Gotbaum governs Gotham." Say that five times fast.