The following are in no particular order (except possibly the first one has potential with the caveats listed), but each may give ideas.
Champion's Taekwondo - I like the fact that it's got a flag in the yin-yang, we could also use a sam-taegeuk. I like the clean modern font, I like the silhouette overlayed kicker idea (but not doing that kick) I don't like the breakout electric text at the bottom.
Sport-Art Taekwondo - clean and simple, I like the use of oriental script at the bottom (it's actually Chinese whereas Taekwondo normally uses Korean script, but for now that doesn't matter)
Israel Taekwondo Federation - I love the kicker in the blue body protector - it's a great kick and anatomically accurate.
Chung-do-kwan - this is a very traditional logo that some people at the club like. The fist image is very traditional, although we'd prefer English at the top to Korean as the club is taught/based in England.
Chang-moo-kwan - as our instructor got his black belt from the Chang-moo-kwan it may be nice if we had a concept that had a nod to the Changmookwan. As an idea, the rearing lions could be replaced with rearing stags/dears as we're based in Hertfordshire, UK which has a stag (actually a Hert) as it's logo.
USA Taekwondo Centers - I like the way the flag and kicker comes out of it's traditional bounding circle.
If you're going to use a Yin-yang, please make sure that red is on top (as it is on the Korean flag). If you're going to use a sam-taegeuk please keep the yellow on top and make sure the red is red. I quite like the idea of the sam-taegeuk in the logo.
If you're going to use a flag it should be the Union Jack (technically the Union Flag).