I know I'm missing something very simple here, but when my anyconnect client is connected, I can't surf the internet. As soon as I disconnect, internet surfing is back to normal. I've looked through the ASDM and I can't find the setting to allow me to surf. What am I over looking?
Try using split tunneling:
Unless you want all your internet connectivity to go over the VPN while connected, in which case you would have to use u-turning: