I live in a small town near Boonville and work at one of the schools (lunch lady). Here is the web site for the school:
http://www.bhs.boonville.k12.mo.us/. Don't hesitate to contact the school directly. The superintendent is a very nice man, and would probably be happy to visit with you about the district.
There is very active and very successfull baseball, football, and other sports programs in Boonville. Some of them are throught the Y:
http://www.boonvilleymca.org/index.p...id=1&Itemid=30. As I do not have a boy, I can't remember if they have Little League for baseball, or if it's Babe Ruth, but I do know that some of the teams have gone to out-of-state regional tournaments, and one team in the past few years made it to the World Series.
There are also a lot of cultural/historical happenings in Boonville, lots of festivals throughout the year. It's just a short drive to Columbia, so I think Boonville/Cooper County should be high on your list to move to. Before you make a decision, look at the taxes comparing Boone County to Cooper County (or whichever county you decide to move to). Boone County has much higher taxes.
Good luck on finding the right home for you and your family!