One of my favorite places to visit in Southern California is Griffith Park. The park is home of the Griffith Observatory and the best view of the world recognized Hollywood sign. The observatory houses many interesting astronomy exhibits which will keep all ages entertained. On the outside, the views of the city and surrounding area are pretty spectacular. Over 50 miles of well maintained trails utilized for running, hiking, and horseback riding surround the observatory. It's the perfect location for a full day of sightseeing and exercise for your family. If you manage to have a little extra time, then Hollywood is only 4 miles down the road. It's a perfect inexpensive day trip.
I can't recommend this day trip enough.
LA gets a pretty bad wrap but there are some cool hidden gems.
This is one!