The WEB's Secret Base is located on the islands surrounding Mulch Island.
It is seen in the SWS Mission The Hunt for Weevil X.
It has a wooden bridge, which beyond you will find Thuggs guarding it day and night.
When you get inside, you will find Weevil X working at the controls. You create a distraction by pressing a button, and Weevil X goes to see what's going on. You quickly press another button, and shut Weevil X inside. You then set the controls of the Secret Base to self-destruct. The mission is then completed. You get a trophy of the WEB's Secret Base and when you click it, it explodes.