Is the "public network" text highlighted yellow not clickable on your installation? On mine I can click on it and change the network type.
Have you tried removing the network adapter drivers from device manager and let it get detected again on the next reboot? It should ask you how you want to configure it the first time it is detected. It seems strange it is showing as unidentified, which seems to be causing the problem.
Hi, TigerTeal over NeoWin helped me sorting out this. And below are the things I learnt;
1. Windows 7 will not let you change the location type until it determines the network's name (or at least not as UNDEFINED NETWORK);
2. To manage Windows 7 to get the network name, unlike WinXP, you must have a default gateway for the connection you are dealing with;
In my case, I didn't put any default gateway for my WiFi network, because I don't need one, I just needed the system to connect to the WiFi network and it was connecting and I could use all the network resources. But that scenario confused Windows 7 as it couldn't find a default gateway for the WiFi network, thus it failed to recongnize the network, because it needs to talk to the gateway to recognize a network, and thus it was labeling it as UNDEFINED NETWORK and was resulting into a READ ONLY network location type for the WiFi network that I was unable to change. I just put in my Access Point's IP in the default gateway box for the WiFi adopter and Windows 7 was able to recognize the network within 2 seconds and allowed me to change the location type straigh way without any trouble.
I think Microsoft implemented this sort of network binding rule and/or topology in Windows 7 for the for the first time, but am not gonna like it, because it will definitely be resulting into side effects like;
a. Interruption with the main internet connectivity;
b. Ghost UNDEFINED NETWORK for the same adopter;