Thanks - What do you mean by league games? Are you talking about little league games? Or are you talking about scrimmages with other local teams?
In the St. Louis area we have "travel ball leagues" for lack of a better term. At least at 10u and 12u we have them. I think there are 2 or 3 different facilities that have these leagues, and you can try to find the league that best fits your level of competition. This year we are playing a double header every Thursday night against other local teams from April through June. (I'm guessing most teams are located within an hour drive) You will usually have 5 or 6 teams in your league.