There's a common way to do it - it's a trick! Even normal GUI's often use this approach:
Basically, you create a text box control and a droplist control and locate them at the same place. By setting up the right event handlers, you move them up or down on the Z axis for the page so that subsequent UI events go into one or the other. Then, on top of that, if the action was a list selection, you'd make its event handler copy the selected text into the text edit box control so that the text box would be the one-stop location for getting results.
An IDE is no substitute for an Intelligent Developer.
Yeah, we are looking for the same thing. And there might be a third part component already out there. But this is probably best done as a custom component, but just Tim explained. I was actually thinking on creating one for RichFaces to adding it to their list of components, just don't have the time for it for a couple weeks.