we have been told that we should present ourselves at the police station
Really? No-one told me that. And we have a few friends who moved out here and didn't do that either. We've been in Limassol since last November and don't even know where the Police station is...
Saying that, we did get immigration sorted immediately. Was pretty straight forward. Immigration office is opposite an Orphanides above an electric shop with minimum ways of recognising it as such (probably doesn't help you at the minute...). Just get there early or bring a book/mobile game. And if you get the bloke at reception then be nice as he is a well grumpy git.
Cheers