Yes it is very close to the Dodger stadium. If you want to be close to Grace Simons find a hotel that is relatively close to Dodger stadium and you will be ok.
Chinatown is the closest. Check the New Otani hotel in Little Tokyo. Lots of hotels in downtown proper including the Biltmore, the Bonaventure, the Omni and many more.
Yes, it is close to Dodger Stadium. If you get a hotel close to Downtown LA its about 10 minutes on the freeway from there
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