That's an interesting question, partially because I might be one of the few holdouts left on the planet who doesn't watch crime dramas and has never seen an episode of any of the Crime Scene Investigation series. However, that doesn't stop me from digging around on the Internet...

My first stop is the always useful Internet Movie Database, which also often has quite a bit of information about TV shows too. A general search for "CSI" reveals the three shows you mention, but also pulls up the name of the show's creator, Anthony Zuiker.

It's easy to then go back to Google and search for his name coupled with "csi" again and find lots of fan sites, but instead, a quick visit to Wikipedia reveals some interesting facts:

"CSI was presented for review to ABC in 1999, only to be dismissed as too confusing for the average viewer. Creator Anthony E. Zuiker then took the show to CBS, which placed it in its Friday lineup, where it shot to the top of the ratings charts. After its initial success, the show's time slot was moved to Thursdays in 2000 in an attempt to challenge NBC's Thursday lineup, which boasted popular shows such as Friends, Will & Grace, and ER. CSI maintained its ratings in its new timeslot, and when Friends came to an end in 2004, its ratings strengthened.

"In 2003, CBS's then-corporate sibling Spike TV purchased the right to syndicate CSI for a record amount of $1.6 million per episode. The nightly reruns quickly became that network's top-rated show outside of WWE RAW.

"Although the show is set in Las Vegas, Nevada, the production is actually based in Universal City, California. In May 2005, it was announced that the sound stage would be moving from Santa Clarita Studios to Universal Studios. CSI began production at Santa Clarita Studios in 1999. CSI is still expected to film on location in Santa Clarita because of its resemblance to the outskirts of Las Vegas. No reason was given for the move.

"In July 2004, CBS briefly fired stars George Eads and Jorja Fox, allegedly over contract disputes. In addition, Eads had reportedly been hours late for work on the first day of filming for the fifth season, and Fox had allegedly failed to submit a letter to CBS confirming that she would be on time for shooting. The disputes were resolved in just over a week, and the two were rehired by CBS.

"As for the show's broader social impact, it has been credited with an increase in college applications to forensic science programs, and has influenced the way victims, jurors, prosecutors and the general public view forensic science. This has been called the CSI effect."

Useful. In terms of your specific question, though, it appears that all the sources are in agreement that there are three shows, CSI: Crime Scene Investigation, which takes place in Las Vegas, Nevada, CSI: Miami, which takes place in Florida, and CSI:New York. There is a computer game called CSI: Dark Motives, but that's about all I can dig up.

Hope that's helpful. Seems like you're getting all the CSI you can possibly get there Down Under. Just don't assume that every town in the United States is as violent and dangerous as what you see on the telly, okay? :-)