I'm not sure what mountain you're planning on hitting the most, but I would check a couple places.NASTAR.com
Good intro to the sport, and some of the races get fairly competitive. Mostly GS. A fun way for the whole family to race together.US Masters website
Depending on your age, this might also be an option. Masters offers coaching, which is a big advantage over NASTAR. In my experience, the courses are more technical and slalom courses are mixed in with the GS.
Town Leagues -
A lot of resorts host "town league" races, which are another source of gate bashing. They vary from resort to resort, and they usually aren't advertised all that well to anyone but ski town locals, but they are worth seeking out.
Ski Clubs -
A given resort usually has one or two ski clubs associated with it, and you can usually find them through their website. If they don't host races themselves, they usually know where to find them.
Hope this helps.