So many people rush to Tianzi Fang or Xintiandi when they visit Shanghai in order to get a feel of the Shikumen style of old Shanghai. However both are now overly exploited, you will see some old buildings yes, but it's filled with businesses and no locals actually live there anymore. They are fun to see but often crowded.
A great alternative for you to see Shanghai's past as authentic as possible is the Sikumen area behind West Nanjing Road. It's still residential, locals still live there, and you see very little tourists there.
You can reach it by taking metro to West Nanjing Road station (M2, 12, 13) and navigate towards Wujiang Road (吴江路) or Zhang Yuan(张园), they are on the edges of the area I'm speaking of, so they are still commercialized with restaurants and bars. Keep walking and follow local looking people, don't be intimidated to get into the local lanes, get lost and enjoy!