First, I'd like to say that it's great you're venturing out of
Disneyland. One of the main differences between the DLR and WDW is WDW is a vacation destination and the DLR is an
attraction of a vacation destination, which is California.
There's not much to do in Anaheim itself, but the good thing is there are lots of activities to do that aren't far at all from Anaheim. I'd go north from Anaheim and visit the Los Angeles and Hollywood area. You could take a Los Angeles/Hollywood tour. So many popular places and landmarks you could visit. Beverly Hills, museums, the Grove, Hollywood and Highland, multiple studio tours, Universal... The possibilities are endless. Not to mention all the popular SoCal places you could visit, like In-N-Out, Tommy's, Pink's, Roscoe's, etc. I love the Disney Soda Fountain in Hollywood. If you REALLY want to go way north, then San Francisco is a must. I love Frisco. Pier 39, the Golden Gate Bridge, great places to eat and not to mention, the Disney Family Museum.
Going more south of Anaheim, San Diego is amazing. Again, great places to eat and fun things to do, like the zoo, Sea World, Old Town, etc.