I'm using Eclipse Java EE IDE and launch Tomcat from the Server's tab on Eclipse.
Where does Eclipse store generated servlet .java files for JSP files? I've checked the Tomcat installation directory, but nothing there.
Doubleclick the server entry in Servers view and check the path represented by Server path. Explore in there from inside the workspace directory. The generated classes are there.
If you choose the 2nd option Use Tomcat installation, then it will be available Tomcat's
/work folder, there where you expected it to be.