I was trying this out, and, I'm pretty sure it's correct (please correct if I'm wrong): Some good places to play harmonics are at the 5th, 7th, 9th, and 12th frets. An easy scheme for determining what harmonic note you're playing is, on a four stringer:

5th fret: is the note of that open string
7th fret: is the note of the string being played on it's 7th fret (on the G string, it would be a D harmonic)
9th fret: this one is will be the major third of the note on the 9th fret of the string you're playing
12th fret: is the note of that open string

Right?

And, remember to crank those highs and play near the bridge!

Yes you got it !
But you can get the same notes closer to the top nut.
Starting on the 5 th fret you have the root,on 4 th you get the third,on 3rd you get the fifth, past the 3rd you get the b7,further up you get the octave ,then the 9th. On a good day(!) you can play a dominant 9 #11 on every string.
Hope this will help
SB

Read here. (http://www.talkbass.com/forum/showthread.php?t=160618)

An addition: Harmonics aren't based on high frequencies. You won't get clearer harmonics by cranking your highs if your mid frequencies are turned down. I'd like you to read my posts in this thread (http://www.talkbass.com/forum/showthread.php?t=157477). The whole thread is very interesting.