The area south from the museums is where real Amsterdam lives and less tourists go. It’s people who don’t want to live right smack in the center (canal area) but still be walking distance to where the action is. A more upscale area with cute butcher, bakeries and vegetable stores and neighbourhood restaurants of all sorts to pick from.
Once you hit the van Baerle straat you are on the border [find Zabars, Renzo’s and Wildshut for the authentic Oud-Zuid experience, or late dining at Bark], and can venture further south onto Cornelis Schuyt straat for more. Veer back to the center via the Vondelpark in summer (or start from there during winter) to have a coffee at the Film Museum’s Vertigo.