Christopher, Cache Creek BLM land (where we are having our annual BPL gathering) is close to Napa. As for backpacking around Napa-Sonoma, I really cannot think of many places to go. Rick is right, you could go to Coe, or Ventana Wilderneess. If you go to Ventana Wilderness you have some wonderful wine country to do wine tasting. The Santa Lucia Highlands is a fantastic AVA for Pinot and Chard. Many great wineries are in that area, namely Pesagno, Paraiso, Bernardus, Figge, Hahn, Talbott etc. All have great tasting rooms and are more in line with how Sonoma is, ie low tasting fees and a more personalized tasting experience.
If you go to Coe or Big Basin, you have the fantastic Santa Cruz Mtns. AVA...wineries include Ridge, Savannah Chavelle, David Bruce, Thomas Fogarty, Bargetto, Cinnabar, Fleming Jenkins, Burrell School, Silver Mountain, Beauregard, Hallcrest, or you can go into Santa Cruz where they have many great tasting facility that houses about 10 wineries which include Bonny Doon and many others.
If you have any questions about the wineries and areas I have mentioned, please feel free to ask. The same goes for the Napa, Sonoma, or Livermore Valley AVA's
I work in the wine business.