I shoot at USI in Concord, and I'll tell you what I can about it. First of all, USI (United Sportsmen's Inc.) is an non profit corporation that owns the land and facilities. 4 clubs operate out of that location, Diablo Rod and Gun Club, Walnut Creek Rod and Gun Club, Concord Rod and Gun Club and Bay Point Rod and Gun Club. If you shoot any kind of guns very often , it quickly pays off to become a member of one of these clubs. I believe you MUST become a member to shoot in a Skeet league.
Skeet is pretty clearly the focus of shotgunning at USI. They have have 5 Skeet fields, 3 Trap fields and one newly redone 5 stand field. They hold 3 registered skeet events each year and a number of other, open events which are non registered club events. They typically have one of these events each month spring through fall.
One of the greatest things about USI and it's affiliated clubs is their policy on kids shooting. I was just about to put up a post relating to this but have yet to write it. Look for it under my moniker later this morning.
USI is probably the closest facility to you for shooting skeet. I will be shooting some later today and if you are interested, you are welcome to come up and join me, my son and another friend for a couple of rounds. PM me if you are interested and I'll give you my phone number.
Price for skeet is seven or eight bucks for non members (I can't remember which) and 5 bucks per round for members, four bucks for kids of members. 5 stand is 7 bucks.
Oh yeah, I almost forgot your original question. Skeet league runs in the spring only and lasts not more than a couple of months. You can find out more about it at the range.