I think there's a black panther exhibit at the oakland museum going on right now. After that you can check out Lake Merritt which is close by. From the Lake, you can cruise up e14/International and hit a taco truck, Sinaloa's is good, or go to Guadalajara, which is a bomb mexican restaurant nearby. In n Out is a close drive away as well, if you're curious about trying it.
In Berkeley, my favorite restaurant is Stella Nonna. It's in my neighborhood, I'd grab a bite with you. The UC Berkeley campus is nice and you can check out Telegraph ave, though it's not nearly as dope as it used to be.
If you smoke, there's BPG (Berkeley Patient's Group), or you can go to eaze.com and have some delivered to your door in twenty minutes.
For some nature, if you're mobile, Cataract Falls in Marin is an amazing hike, if not a bit far out. You can drive the golden gate bridge afterwards.
For nightlife, you can head out to Oakland and hit up Era, Lieg, New Karibbean City, Somar for clubbing