OP doesn't have "Find my iPhone" activated on the device??? It's trackable whenever it gets connected to the internet by any means. if it hasn't shown up, it probably means it's sitting in a locker at a lost-and-found office somewhere.

I also have a screen saver with my contact information.

>> how to buy a new one?

I think BIC/Yodobashi sell used ones, but they are SIM-locked to local network. I doubt that they require a contract.

Otherwise you need to look for a store that sells "white ROM"(meaning unlocked) phones, such as http://kaitorishonen.com/ , or on amazon.co.jp (search for "iphone 4s 白ロム ")

2nd hand chain shop http://sirorom.e-daikoku.com/index.jsp may carry unlocked ones. They have branches everywhere.