I got my band done in Italy with Dr. Favaretti and Dr. Segato. They are leading lap band surgeons who trained many american and mexican doctors. LAP-BAND: Laparoscopic Obesity Surgery Cost
It was 12,000 US for everything to do with surgery, hospital tests etc... You just have to pay to get to venice. If you can find good aftercare near your house this is a great option. The are amazing Doctors. They like you to stick around for a few days after you are released from hospital to keep an eye on you but you could combine it with a vacation and enjoy italy.