Unfortunately there aren't too many stop motion studios left, even in the LA area. A lot have transitioned to CG and digital 2D. But, the ones that I know still operating are:
Bix Pix -- http://www.bixpix.com/
Stoopid Buddy Stoodios -- http://www.leagueofbuddies.com/ (they have a fantastic intership program. Albeit selective, but I've heard wonderful things if you can get one there)
Shadowmachine -- http://www.shadowmachine.com/#/contact (I think they're slowly becoming more of a 2D/CG studio now, however, they are currently producing Guillermo Del Toro's Pinnochio and helped produce Hell & Back so stop motion has not gone away completely)
Screen Novelties -- http://screen-novelties.com/contact/jobs/
Those are the "big" ones that I can think of that I'm fairly sure all take on interns. I imagine there are a handful of other tiny studios, and positive that LOADS more large studios doing digital 2D and CG animation in the area are also looking for interns.
Thank you so much :)