Everything looks good, so something else must be up here.
Lets take a closer look at your Network System Preferences...
You mentioned that your ethernet was working, how about deactivating it in your current location, so only the Airport is active. Highlight the Built-in ETHERNET, and click on the little gear at the bottom of the column, then select "Make Service Inactive".
Then click on Airport, and the Advanced button.
Click on the TCP/IP tab, and use these settings:
Configure IPv4: Manually
IPv4 Address: 192.168.0.57
Subnet Mask: 255.255.255.0
Router: 192.168.0.1
Configure IPV6: Off
Click on the DNS tab, and make sure you have 192.168.0.1 listed as a server.
Click on the Ethernet Tab, and make sure you have Configure: Manually, and MTU at Standard (1500).
Click OK, and Apply.
Give it a second, and then try to ping 192.168.0.1...and let us know what happens...