You should probably do artists who are more relevant... BoA isn't relevant anymore, and TVXQ aren't as "cool and trendy" as they used to be.
I would say pick one SM group, if any (since all their music for the past year is pretty much the same anyways). SNSD might be a good choice to show off the "cute" side of k-pop with a song like Gee or OH! But if you put something cutesy in, try to stick it like somewhere in the middle so if people don't like it, they'll be less likely to remember it and base their opinion on k-pop off it, lol.
2NE1 or BIGBANG (one or the other) is good for the 2NE1/BB style. Please just, if you pick 2NE1, DON'T show them I AM THE BEST.
I'm not kidding, only 2NE1 fans like that song. Show them a song where the chorus
isn't just the same 3 words repeated over and over again. If it were me, I'd pick Can't Nobody.
Since 2PM is one of the strongest groups as far as dancing goes, one of their MVs with good choreography would be ideal for showing off the dancing aspect of k-pop. T-ara would be good for the sexy, electropop, trendy side. I also kind of agree with the CNBlue suggestion, just to show a more pop/rock side.
If you want to go with a solo artist, I would say Lee Hyori (even though out of BoA/Dambi/Hyori, she's my least favorite). She's probably the one that would be most popular with Americans who aren't really into Asian music or style. U-Go-Girl might be good, since it's really catchy (and unlike Chitty Chitty Bang Bang, wouldn't get her called a Lady Gaga wannabe, lol).
Try to pick things that are... optimally suited for American tastes. You want to show off real k-pop style, but you don't want people to be turned off by how effeminate the guys can be, weird make-up, etc. 2PM or BIGBANG would be a good choice for boy bands because they have a more manly image in their videos, whereas SHINee would be a really bad choice (I CONSTANTLY overhear all my male friends talking about how "gay" they think SHINee look in their MVs). BEAST or MBLAQ might be a safe "in between" choice, not too effeminate or too manly.
I hope that helps.
I tried not to be too biased, so only two of the groups I suggested are favorites of mine.