I am in Santiago for the summer, and I am hoping to find a wine bar where we can go for tastings of a wide variety of the local offerings. Anyone have any suggestions?

Just a few that spring to mind, by no way an exhaustive list:
360, at the Ritz Hotel (metro El Golf).
Miguel Torres, Isidora Goyonechea (metro El Golf or Tobalaba)
Baco, on Nueva de Lyon, Providencia (metro Los Leones)
De Tapas y Copas, Calle Dardignac
The last two are not wine bars per se, but they have a decent selection of wine (including by the glass).
Other than that, hit your local supermarket, of if looking for something more upscale, Vinoteca o Mundo del Vino. Or go to a winery.