The fastest way to move around the IDE is with the keyboard. Most tool windows have a simple numeric shortcut, for example the Project tool window is ⌘1 (macOS) / Alt+1 (Windows/Linux). For those that don't have a keyboard shortcut, you can open these by using Find Action, or Search Everywhere.

Don't forget, you can easily search any dialog or window in IntelliJ IDEA simply by typing the thing you want to search for.