Most, if not all Apple products, have a 'find my iphone' application on it - which owners should have activated very soon after the iPhone came into their original possession.
If it was activated, then the owner should/will have remotely logged into his iCloud account and viewed where all his activated products are physically located. It's reasonably accurate. The owner can also:
a. Remotely erase the phone.
b. Make the iphone start issuing a regular - annoying - loud bleep.
So, if you hear it bleeping loudly, the owner has probably located roughly where you are so I would stand outside your house if it starts bleeping loudly.
Alternatively you could ring up Apple support, quote the iPhone serial number on the back and ask them to send the owner an email with your contact details. That assumes he has registered his product with Apple. I haven't tried this approach but I don't see why Apple support wouldn't play ball (you can chat to Apple support on-line if you want).
I'm sure you'll let us know how you get on.
PS. I wouldn't put a notice up in the street as I fear you may simply encourage chancers?