Marin County, especially on the slopes of Mount Tamalpais, have the greatest elevation change trails in the Bay Area.
Those communities along the spine of the coast mountains on the San Francisco Peninsula (Portola Valley to Pacifica) also have great access to fabulous trails.
But for the easiest access, living near the ridge in the East Bay (Fremont, Hayward, Castro Valley, San Leandro, Oakland, Berkeley, Richmond) gives access to multiple trails mostly running north-south. Â I’ve walked out of my house in Castro Valley and gone through Chabot, Redwood, Roundtop, Huckleberry, Sibley, Tilden and Wildcat Canyon Regional Parks, turned around and hiked back for a 100k / 62 km day hike staying on trails almost continuously only have to cross a handful of roads. Â Admittedly, even though I was 1/3 my age then, I was sore for 3 days afterwards, but I’m glad I did it. Â Hundreds of times, I’d take more reasonable hikes solo or with friends, usually day hikes but camping and backpacking are allowed there as well. Â It really is a tremendous resource to have such extensive, contiguous wildland adjacent to a thriving metropolitan area. Â The housing near the ridge isn’t cheap but there is public transit (or a 1000-vertical-foot hike) up to the trailheads from the lower-cost flatlands.
Not what most people would call the southwest, but it’s far to your west and 2000 miles to my south.
If by SW you mean AZ and NM, then Flagstaff really stands out for year-round, world-class, multi-sport activities very near by.