Does your community have Youth Lacrosse? It's a great sport for young kids. They get as much running in as soccer, but there is more scoring, so it keeps their attention better.
Plus, because it is still a "niche" sport, most of the coaches and parents are people that really love the sport, and you don't get a lot of asshats, like you do with little league.
Personally, I think you get more bang for your buck with sports that martial arts. And you can change sports with seasons, giving your kid a break from doing the same thing all the time.
Plus, if your kid likes lacrosse, and stays with it, a LOT of good colleges are awarding scholarships for lacrosse players. There is a lot less competition than there is with other sports.