Yet another tack is to list some of what are considered the "best"/most unforgettable hikes in the area. Then, use 511.org to plot out the transport from your location to the trailhead. Decide if it's reasonable haul...or if (alternately) you really need a friend with a car to go there!
My very favorite book is "101 Great Hikes of the San Francisco Bay Area" (by Moon Outdoors). Get it now. It details many of the hikes that follow.
My "Best hikes in the Bay Area" list would include...(mostly these are day hikes)
1. North side Mt. Diablo, any trails, lots of singletrack, climb the mountain or do one of many less ambitious loops. Back Creek Trail and Middle Trail are favorites. Waterfalls loop is nice too. Order a map of Mt. Diablo State Park in advance. You need to get to downtown Clayton (if on transit) or to the end of Regency Drive in Clayton (if driving). Olympia Trail is also fantastic but trailhead is hard to find and you need a car.
2. Steep Ravine Trail/Matt Davis Trail from Pan Toll Ranger Station (along the Panoramic Highway over Mount Tam), or, alternately, you can start/end in Stinson Beach. There is a little bus that runs out to Stinson Beach from Mill Valley and Marin City; 511.org should identify it.
2a. An alternate, similar trip would be to start in downtown Mill Valley, find Old Mill Park, and hike the 7.5 miles of the Dipsea Trail to its end in Stinson Beach.
3. Angel Island State Park. Ferry from downtown Tiburon. Angel Island is more of a long stroll. Good if you're with a friend who's not an uber-hiker. Get to the singletrack.
4. Berry Creek Falls loop, Big Basin State Park. Trail starts at park headquarters in Big Basin. Good overnight option is the backcountry camp ("Sunset") out by the falls.
5. Murietta Falls, from Del Valle Regional Park. Forget public transit; bring a friend with a car, who also doesn't mind hiking straight uphill for 3000+ feet.
6. In Marin County, get to Tennessee Beach and hike to Muir Beach; or get to Muir Beach and hike to Tennessee. The best trail between them is the singletrack that hugs the coastline.
7. Top of Mount Montara. Starting point is San Pedro Valley County Park in Pacifica.
8. Peters Grove, from the main entrance in Portola Redwoods State Park. Car needed. Some day I will bike there from Caltrain.
I've done a hundred hikes in the Bay Area, those are my Top 8 and I'm sticking to them ;) Would love to hear others' opinions here.
The inland hikes (Diablo and Murietta) are far, far more interesting in the spring, with the green and the wildflowers. Go there between February and mid-May. Frankly, I don't bother after May; it's too hot/brown out there.
A bike helps *a lot*. Sometimes I take public transit (most buses have bike racks in front), bike to the trailhead, and either lock the bike up or hide it in the woods. Sometimes this is faster than waiting for the local slow bus; and/or it adds a pretty bike adventure to an already nice hike.
For the Marin hikes, you can ride your bike across the Golden Gate Bridge straight to the trailhead; or cut some time/effort by taking a bus across the Golden Gate and then biking from, say, Marin City or San Rafael to your trailhead. Lots of Peninsula parks (such as Wunderlich Park) are very quickly accessed by bike from Caltrain stations. I've biked to Big Basin but that was a very long haul with a lot of climbing. Buy a bike map of the Peninsula and a bike map of Marin. I've also biked to the Mt. Diablo trailhead in Clayton, by taking BART to Concord Station and riding out Clayton Road.