Q: MacBook air internet not working

This article might have some useful troubleshooting tips: http://support.apple.com/kb/HT1714

NOt sure about public places, but at home what you should do is go to system preferences, then go into network and press the '-' symbol and delete your current wifi connection. Then restart the process of connecting to the internet. Obviously make sure you have latest drivers installed as well, because if it isnt drivers, or your settings, It could very well be hardware, or your router? But you do say your other computer is fine so dont know about it being the router.