New York Magazine casts an eye on the unofficial First Couple of NYC, the Giulianis, with a cover story on all that's known about Judi. Lloyd Grove's article explains about this much:

Their meeting: Neither Rudy nor Judi will talk about exactly what happend, but apparently they met at a cigar bar on the Upper East Side and later went to a movie and dinner at Peter Luger's.
Rudy really loves her
She may or may not be a climber. Judi did fall for Rudy pre-September 11, but one of her ex's friends gives a pretty withering description: "She was a real opportunist, a real Becky Sharp character...I think she really desired to be sort of the Junior League type. She basically struck me as having an inflated, self-important view of herself.”
There's some question about how much Judi Giuliani did post-September 11; while Giuliani claimed she "coordinated the efforts at the Family Assistance Center on Pier 94," former Giuliani-era OEM director Jerry Hauer tells New York he organized it.
Rudy's presidential campaign staffers aren't too fond of her, but one longtime Giuliani aide was allegedly fired after saying, “Let me guess—you’re waiting for Princess, too.”
One of Judi's friends says Judi is upset that she might be a liability (and how her past as a medical supplies executive who stapled live dogs' stomachs during demos keeps percolating up) and the friend suggests, "I think Rudy’s the one that’s sabotaging her. He’s out of control. There’s too much hand-holding and kissing on the lips, behaving like a couple of 18-year-olds in their first love affair. She doesn’t have the political smarts, and I don’t think she expected any of this."

Naturally, a lot of the speculation about Judi is in the context of her as potential First Lady. Which is good copy now, but come on, how likely do you think it is for the Giulianis to move into the White House?