Is there a command or quick-key to bring the playhead's timeline position to the center of the screen?

Also, is there a zoom that will narrow in on that playhead instead of the middle of nowhere? I'm using 'zoom in/out of timeline' currently.

I guess you're referring to Final Cut.

I too, am looking for a similar option and have yet to find it. Have you checked the quick reference guide? I need to take another look at it and see if there's something listed. I'll check tonight

Can't find anything that does what you were looking for, but I did come across "option h" which shows your keyboard map and "shift z" that zooms your entire timeline to fit the window... two I didn't know about. I found the shift Z useful

One of the fixes in FCP 6.0.2 (released last week) is that the zoom in and out work around the playhead. So far, for me, it seems to work (most of the time).

Also, I found the following approach useful:
1. shift z to zoom out to show the entire project in the timeline.
2. select a bunch of clips around the playhead (as many as you're interested seeing at the moment).
3. shift option z to zoom in to those selected clips.

For me this is very quick as I can keep my right hand on the mouse and do the key commands with my left hand.

also in version 6.0.2 is the "scroll to playhead" command which will auto scroll th etimeline to center the playhead ... you can map it to a keystroke in the Tools menu > Keyboard Layout... window