If you're planning to be in Anaheim, CA, it's probably because you're visiting Disneyland or attending a conference at or near the Anaheim Convention Center.
Whether something is near or far depends on your perspective. Compared to the distance from San Francisco, New York or Berlin, Universal Studios Hollywood and the San Diego Zoo are close to Disneyland. But
when you think of "near" as something close enough to do in the same day, or attractions to visit from the same hotel base, neither Universal Studios nor the San Diego Zoo are especially convenient to Disneyland, and if you have the option, I recommend changing hotels, so you don't spend two hours in rush hour traffic trying to make that drive.
If you're staying at a hotel near Disneyland, most Los Angeles attractions are 45 minutes to 2 hours away, but there are plenty of other attractions in and near Anaheim to entertain the whole Family.
On the next pages are some things to do within half an hour of Anaheim (even if you stay off the freeway and take surface streets), arranged by distance from Disneyland.
To plan the Disneyland part of your vacation see my Disneyland Guide
Here's a separate list of Orange County Beaches, the closest of which is about a half hour drive.