CA is amazing for everything described above, and doable from the SV, but it is muchless convenient than I imagine Vancouver Island is. Living in Seattle I can be actively engaged in any of the above with a 45 minute drive or less. From the SV, you are likely looking at a trip to Tahoe for any good climbing, hiking or skiing. It's doable, just not as convenient. (Note: I hate to appeal to authority, but I lived outside Sac for 4 years and Seattle the last year, and it is definitely easier here.)
If your goal is alpine hiking or skiing, then yes, you're going to need to head up to the Sierra. Most good spots are about 100 miles (160km) from the Bay Area. Depending on when you leave and traffic, that's 2.5-6 hours (the last during peak tourist season).
But if you're talking about hiking hills and lower peaks (to ~5,000'), surfing, windsurfing, etc., then from any of the major population areas (San Jose, Penninsula, San Francisco, East Bay), odds are good you're within 45 minutes of good waves, 20 minutes to water period, and in many places, can simply walk to a trailhead.
Sacramento is a good 80 miles from San Francisco, and isn't considered "Silicon Valley" by any means. Even there, you can find recreational cycling pretty much anywhere outside city limits, or the American River Trail. The Sierra's that much closer, with a 1 hour drive up I-80 or US 50 taking you to prime hiking spots.
It's just not inconvenient, it's limiting. You can't exercise while you sit in your car for hours and hours. And more often than not, you will choose to go.
