@CLMM My favorite is Redwood Regional park! It is part of East Bay Regional Parks. Its great for hiking with dogs and has many diffent types a terran. Redwood Regional blends a mix of shaded trials and others that are more sun kissed! There are tons of trails of all difficulty ratings there also.
I love using The Hiking Project app to help me find hikes in the area!
At REI, we believe a life outdoors is a life well-lived.
If you're near Half Moon Bay, Gray Whale Cove trail is a beautiful and relatively easy hike (see picture of Gizmo enjoying it this weekend!) and you can end in a shady spot near McNee ranch. It's not full shade but the ocean breezes keep it cool and you've got dog friendly spots like Moss Beach Distillery, Hop Dogma, and HMB Brewery nearby. Further south towards Santa Cruz the Forest of Nisene (state park) is a much larger network of trails, mostly shade, and is so gorgeous and lush it looks like you stepped into Fern Gully.