I have stayed at the Checkers several times. It is a lovely hotel and about as boutiquey as a Hilton comes. However, I fear you are misjudging L.A.

Hollywood and Beverly Hills are only accessible from downtown via a +/- 1/2 hour car ride (depending on time of day) or, for Hollywood, a 20 minute Red Line subway ride. There are some very nice restaurants downtown and a couple of sights (the Library Building comes to mind) but there is really little reason to stay downtown unless you have business there or are going to see a lot of stage productions and the Dorothy Chandler or Disney theaters.

On the plus side, you would have public transit available to get you to Hollywood, the east San Fernando Valley, or Pasadena. And you would not be too far from the Natural History Museum and California Science Center.