I don't know if this is the closest beach. The locals can correct me if I'm wrong. But we went to Huntington Beach, which was about 25-30 min. away from Anaheim, and stayed there for 2 days. We absolutely loved that beach, which went on for miles and miles. At the end of the pier, there are some great places to eat -- Chimayo's and Duke's (both of which we tried) and Ruby's Diner (we never ate there). Side note: Loved Chimayo's and Duke's but make sure you get reservations if you want to enjoy dinner there or you're outta luck.
The sand at Huntington Beach was so nice and soft. The waves were great for boogie boarding and surfing.