Check out the AHA's Competition Calendar. Also, grab some beer newspapers from your local homebrew store, you'll more than likely see some advertised in there.
Competitions are great feedback and great motivation---if you don't do well, it'll motivate you to improve your beer. If you do well, it'll bolster your brewing self-esteem and make you want to enter more comps and brew more beer. Plus, you can get some cool winnings...cash, hops, shirts, gift certificates, etc.
Note that not all competitions are BJCP-type. Some are "people's choice". So read the fine print, so to speak.