I don't see how that is possible... For one, from what I understand that data you are referring to is probably pulled from cache or cookies on the given system. The only way you could get a zip/postal code or location is if the ISP kept a visible database to trace routes in relation to subnets and location..., which I don't think they do since that would be violation of most end user agreements.
However, I am no expert and please correct me if I'm wrong.
The only other thing would be to locate your local ISP, and that would give your city but nothing more accurate then that.
For instance check here and add 126.96.36.199 (hardocp.com) it will tell you its in Dallas and the ISP is The Planet but not much more.
Windows local live http://local.live.com/ has a "locate me" button which if you don't install the activex control will try to work via ip address. I believe I read somewhere how to just feed it an ip address and get back a location. This of course doesn't work quite right for every ip address since I think it works by the company that owns the IP but that might be close enough.