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IMO the OP is trying to do far too much in 7-8 or even 10 days.
One day isn't enough for SF and anyone interested in wine can happily spend a week or more in Napa and Sonoma. There's also some wine in Mendicino, farther up the coast from Sonoma and some areas with big trees. Sausalito is also a nice stop, just north of SF.
If you really want to cover more territory or if using the San Jose airport makes sense, there's wine and scenery along the coast to the south (Monterey, Big Sur/Asilomar/Santa Cruz, Central Coast, Santa Barbara, etc.).