I think the only EUG nonstops to/from the Bay Area service SFO. That said, the SFO/Marin drive can be unpleasant depending on time of day. You've either got a big chunk of non-freeway through SF or going via the East Bay for freeway the entire route. Depending on fares/timing, a connection to get to STS may be your best bet. The only chokepoint most times is the construction area on 101 near Petaluma. Travel to/from OAK or SFO during many points during the day could provide one of California's great traffic jams.