SSID is "visible" whether you choose to actively advertise (broadcast) it or not http://www.wi-fiplanet.com/tutorials/article.php/3576541. Leaving it switched on as it makes it a lot easier to figure out which network you are connected to, turning it off doesn't really buy much in terms of security against the determined hacker.
In most environments the best advice is to use WPA wireless network encryption to keep your WLAN private and secure. WEP can be defeated very quickly, and in a busy WiFi environment, could be a tempting target - http://practicallynetworked.webopedia.com/TERM/W/WPA.html
Thus where WPA is available you need to configure the Wireless Router / Access Point (WAP) to enable WPA, enter a strong password (see below) and then enter the same password on your PC (on the wireless adaptor configuration). It is also probably best to store it in a file somewhere discreetly in case you forget it.
Use http://www.soroban.co.uk/wepkeygen.htm to generate WPA keys - it's free, but does require MS .NET Framework to be installed on your PC. Google for WPA Passphrase if you want to check out other software.
Where WPA is not available then configure the Wireless Router / Access Point (WAP) to enable WEP, again enter a strong password and then enter the same password on the wireless adaptor.