Really slow kicking.
There are also several really good 'gadgets.'
Standing on one of those balance board things and trying to kick is a good challenge.
I like these downhill ski machines that some people make.
I use one at my gym. It saves time because you get cardio at the same time.
Slacklining is also a very challenging balance activity.
Here is a link to some slackline equitpment and balance boards: http://www.mountaingear.com/pages/produc...alance+training
Finally, try yoga. There are some incredible balance training postures in yoga.
As far as closing your eyes, I don't think it's necessary.
It makes it harder because it decreases spatial awareness, but it won't necessarilly translate to better balance when your eyes are open.