Welcome to my neighborhood! I like the GG Park suggestion (the Academy of Sciences is a must if you're at the park) and Lands End is beautiful as well. Walking the Golden Gate Bridge is awesome too especially on a nice, clear day. The rest probably depends on how you like spending time when you travel. If you like touristy places, you can walk up Telegraph hill to Coit Tower, drive down Lombard, walk around Pier 39, reserve an Alcatraz tour (if they're not already sold out), etc. If you like baseball, I'd highly recommend catching a Giants game, the ballpark is awesome.
If you want to do less touristy stuff and hang out in local spots, I'd walk around the Marina and catch lunch at one of the cafes. Crissy Field is nearby as well. You can rent bikes from Sports Basement and ride around 'til you can't anymore! Since you'd be close to the Golden Gate Bridge, you could rent bikes and ride across instead of walking if you feel like climbing some hills initially. Fort Funston is a fun beach walk and is also dog-heaven if you guys like dogs. For a twistier driving experience, head to Vermont street on Potrero Hill instead of Lombard. If you want to head outside of SF, drive some sweet roads and catch a delicious and relaxing lunch, go to Alice's Cafe at 4-Corners (Hwy 84 & 35). It's a well-known hangout for bike riders and car guys. If you want quiet and peaceful, go during the week. If you want to see some action and meet a bunch of like-minded people, head up on a weekend.
There's a ton of stuff to do, honestly. If you have any questions, just send me a PM or give me a call at 650-438-0224! I'd be happy to have you come by my place and talk Zs for a minute or two if you'd be so inclined. I work at Sears Point/Infineon/Sonoma Raceway so you're free to come by for lunch sometime and check out the shop as well. I'm camping 7/25-27 but will be back home Sunday night.