The intensely atmospheric teahouse inside the Panama Hotel has such a thoroughly back-in-time feel that you'll be reluctant to pull out your laptop (although there is wi-fi). It's in a National Treasure–designated 1910 building containing the only remaining Japanese bathhouse in the US, and doubles as a memorial to the neighborhood's Japanese residents forced into internment camps during WWII.
The beautifully relaxed cafe has a wide selection of teas, pastries, and Lavazza coffee.