If you decide to go to Beverly Hills, this is a DONT MISS! It is an estate owned by the city called Greystone Mansion. It is an amazing beautiful place. We go there often to walk around. Although you cannot go inside, the grounds are lovely and provides a huge bit of history.
If you are in the area, you can drive east on Sunset blvd. for about 6 miles, and turn Left onto La Brea, Turn right on Hollywood blvd. and check out Manns Chinese theater, the walk of fame, Kodak theater, etc. A few historic great places to lunch are:
Musso and Franks - a bit spendy but you can google their menu and any menu for that matter, at menupages.com
25 degrees at the Roosevelt hotel- pretty inexpensive , huge portions. The hotel is also a huge historic building.
The Pig and Whistle- fun place, original booths from the first restaurant of the same name, 1920's.
Micellis- Great itallian place, very old school hollywood.
Okay, then, after you have eaten, continue east on Hollywood blvd, and make a left onto Gower, and a right onto franklin. when you get to beachwood, make a left and you can go up to see Griffith Park observatory, and the Hollywood sign.
As you can tell, I love my town. I hope this helps!