You can drive all the way to the top and the view is amazing!! You can see across the whole valley! There are also great hiking trails all along the road.
Muir woods is a bit longer of a drive, about 45 minutes away but it is worth it if you want to see redwoods. You can walk through the redwoods here and see where we took some of our engagement pictures.
Great place to get food, lots of amazing restaurants, some of our favorites being Limon, Opa!, Burma 2 and El Charro. It is a bit more on the expensive side though.
If you are looking to go into the city i would highly recommend going to the ferry building and walking along the piers. The ferry building itself has a lot of good food and cool shops, you can also get there easily through BART by getting off at the Embarcadero Station.
The outdoor shopping mall in downtown Walnut Creek. There are lots of really cool stores to find all kinds of things in whether it be clothes or something more niche like handcrafted cutting boards with a "river" through them.
A nice, easy and fun hiking experience if you go straight through Castle rock park.