Yes!
Here are three good ones. The first two fall more on the easy end of class 3, while the latter is tougher.
First -- for my money the best one-day loop within day-trip range of the Bay Area is a traverse of the Crystal Range in the Desolation Wilderness. Start from the Wright Lake trailhead. Hike in to (??) lake, and leave the trail to ascend to the west ridge of Mt. Price. Summit Price, follow the ridge to the summit of Mt. Agassiz, then follow the long ridge toward Pyramid Peak. The hardest scrambling comes as you approach the lowest col on that ridge. Ascent Pyramid via the steep north ridge, descend the scree west slope to (??) lake -- I forget all these names -- and follow trails, one down a creek and the other a very level crossover leading north, back to your trailhead. A wonderful day. All three peaks are just under 10,000 feet, so acclimation issues in a one-day venture from the Bay Area are unlikely to kick your butt the way they easily can if you go much higher.
Second -- go through Tuolumne Meadows and out the other side of Tioga Pass (now we're talking about Yosemite) and turn north for the Saddlebag Lake trailhead. This one goes better with a night or two to spend. Pitch a camp at one of the lakes in the basin framed by Mt. Conness and North Peak. Climb the east-southeast ridge of Mt. Conness. This joins the south ridge just above 12,000' and then you can easily follow a use path to the summit at around 12,600. The hardest parts are in the middle of the ridge; staying near the ridge crest puts you squarely in class 4 territory, while descending off the crest to the south lets you work around the towers and gaps and keep it in easier class 2-3 territory.
Third -- the east couloir of Mt. Sill is a pretty awesome route. Look this one up in Secor's guide, the approach is more involved than I can remember off the top of my head. This gets you up really high (Sill is a 14-er) and the trailhead is a long way from the Bay so it helps to have a few days.
