Nice, Jinal!  You've got so many options around here.  

You could do an East Bay trip.  Right across the Bay Bridge from San Francisco, there's Oakland.  Jack London Square is notable there with a nice waterfront and plenty of restaurants and cafes.  There's also Alameda, which is a nice little downtown area on Park St.  Close by is Berkeley.  Downtown Berkeley is lovely.  You can also visit UC Berkeley campus for their amazing architecture, Telegraph Ave for some local flavor, or even go hiking in the Berkeley hills.

Up in the North Bay, you've got Marin Headlands, Muir Woods National Monument, Stinson Beach, and the adorable towns of Tiburon and Sausalito.  I actually rode my bike across the Golden Gate Bridge to Tiburon this weekend for brunch, so that's one possibility.A bit further up north is Sonoma and Napa wine country, if you want to do some wine tasting and while taking in the north bay sun.If you venture down south, there's the Peninsula, where you can visit San Mateo and Palo Alto, which are more techy towns.  But for a vacation, I suggest going even further south to some beach towns, such as Monterey, Santa Cruz, and Big Sur, the latter of which is about a 3 hour drive from San Francisco and worth an overnight trip (though I've done day trips before).  It's worth it.When you decide where to go, you should post another question to let us know where and we can help you out with more specifics! :)

North of San Francisco, in addition to the Marin County towns mentioned by Debbie,  Petalumaand Healdsburg are two awesome destinations.  Petaluma has a pretty Victorian downtown area, good restaurants and shops, some interesting sites and Lagunitas Brewing Company, which is a great place to visit if you are a beer drinker.  They often have entertainment going so check if you are interested. 

Healdsburg is in the heart of the Sonoma Wine Country with many, many wineries close by, but it doesn't seem as touristy as Napa.  The downtown is very charming and there are many great restaurants and shops.  Scopais a fine, casual restaurant with an outstanding Sugo Calabreseand Pliny the Elder, from the nearby Russian River Brewing Company, by the bottle.

I would also say Calistoga. It is a great little town. Indulge yourself with a mud bath/spa day Dr. Wilkinson's Hot Springs Resort. It is excellent. It is also a good base to discover the Napa Valley wine country, maybe take a tour or rent a bike. Have fun

I would echo what Debbie told you: Calistoga is a great little town for dining and spa activities. Plus the wineries are awesome!  Santa Cruz is a great base to see the big sur area . Julia Pfeiffer Burns State Park is outstanding. What few people know is that the cafe inside the park headquarters is a gem of a dining spot.

I thoroughly recommend a west Marin, highway one day trip, or overnighter including stops at Point Reyes Station, Bolinas Bay, and Bodega. Highway one runs along the coast all the way. It's a drive you'll never forget. If you've got time, add another day and head east from Bodega toward Sonoma and  Napa wine country. You could take a week doing this drive and still wish you had more time.

There are so many interesting towns and areas to visit outside of San Francisco. One of my favorites is Sonoma county where I lived for about 10 years. If you are into wine tasting or not, I wrote a post about Sonoma attractions, you can check it out here. http://travelphotodiscovery.com/10-things-to-do-in-sonoma-without-tasting-the-wines/

Point Reyes is also close by in Marin, here's a cool town you can also visit and see the national park afterwards

http://travelphotodiscovery.com/visiting-point-reyes-station-travel-photo-mondays/

You can check out my blog for more information on Northern California and enjoy.

Lots of great answers here so far. As far as wine country goes, Healdsburg, is by far my favorite town in Sonoma and Napa. I love taking the ferry from SF to Sausalito, which has some cool restaurants. Bar Bocce in particular is fun on a warm day. Other towns I dig include Mill Valley (often hang here after hiking Mt. Tam) and Half Moon Bay, which is a charming beach town just south of SF. 

If you want to stay closer to SF, you can always head east to Livermore It's a great small-er city with a cute downtown area and some great wineries to visit. And, without traffic it's less than an hour drive from SF.