Basically, there are decent parks that are right in town, great parks that are within an hour or two, and mind-blowing, spectacular parks within 5 hours.
Right in town - Lots of big trees and green in Golden Gate Park and the Presidio. I run through GGP regularly and maybe I'm running in the wrong (right) places, but I see far more homeless in the inner neighborhoods.
Close by - Marin! Muir Woods is the classic, but there are plenty of other great possibilities. My top recommendation would be to hike from Stinson Beach up to the top of Mt. Tamalpais and back. It will give you a good sense of most of the terrain in Marin County, and the Steep Ravine trail is simply gorgeous. Also in Marin, if you get out to Point Reyes, there is hiking and rugged wilderness for days. I would recommend the Tomales Point trail, which runs right through an Elk sanctuary, and at this time of year the lupine may be in full bloom. It is surreal. The end of the trail is a point where you could drop 300' down to the Pacific Ocean on your left and Tomales Bay on your right. Another great Point Reyes destination is Alamere Falls, one of two nearby waterfalls that drop straight into the ocean, the other being in...
Big Sur! Breathtaking coastline where mountains meet water. McWay Falls is right off the highway, but basically, you can pull over at any trailhead and start hiking and have a great experience.
There are also very nice places in the Santa Cruz Mountains like Big Basin Redwoods that fall within this "1-2 hour drive from SF" category
Also worth mentioning, if only because you can do it completely without a car, is that Tilden Park is the ridgeline high above Berkeley, and you can get there pretty easily by taking the BART to Downtown Berkeley, then transferring to the 65 or 67 bus. There is enough wilderness to get lost in up there.
Also, much of Marin is potentially accessible without a car, but you'll need to work at it. Check out Marin Transit http://www.marintransit.org/routes/66.html
for the Muir Woods shuttle and the West Marin Stagecoach.
Finally, we have wilderness within a 3-5 hour drive that would blow anyone's mind. There are many tour companies that will give you great prices on bus trips to the Sierra for hiking or rafting or whatnot. Check out Bay Area Ski Bus for example:http://www.bayareaskibus.com/index.cfm/summer_trip_adventures.htm
But if you do decide to drive somewhere yourself...
Yosemite Valley, Tuolumne Meadows, Kings Canyon (especially around Cedar Grove), Sequoia National Park (the Giant Forest Museum is right off the road, then you can pick up the High Sierra Trail and do a long dayhike with spectacular scenery) the Lake Tahoe Basin (especially Desolation Wilderness), even random-ass canyons in the Sierra foothills within an hour of Sacramento are gorgeous. Twice in the past month I've spent weekends backpacking up in the Trinity Alps, which is also spectacular. But it's further than the Sierra, so probably not worth the trip if you only have 2 weeks - I only took my trips there because of inclement weather in Tuolumne.