Im not sure what your budget is, but there are some great little boutique hotels in the city. As far as staying outside of SF, how close are we talking. IMHO, the surrounding cities aren't the greatest. How far are you willing to be from SF?
While in SF, you must drive over the Golden Gate bridge; its just timeless.
There are a few wineries that I just adore: I Love going to Mumms, sitting outside enjoying some wonderful champagne. April can be so beautiful in Napa. Near Mumms is Miner Family Vineyards. I love their tasting room, and you get an amazing view to boot. I adore their red wines, as well as their white. I also suggest Cliff Lede Vineyards. Very quaint and the grounds are gorgeous. My sister found bothe Miner and Lede totally randomly, and they both make the most delicious wines.
http://www.cliffledevineyards.com/ [nofollow] http://www.minerwines.com/index.html [nofollow] http://mummnapa.com/ [nofollow] In Yountville, which is right near Napa, you HAVE to go to Bouchon bakery. The last time we went, we stopped off for some wine tastings, picked up a couple of bottles and went to Bouchon for some sandwiches and sweets. Absolutely delicious. There is a main restaurant, but I am talking specifically about the Bakery, which is next door.
http://www.opentable.com/rest_profile.aspx?rid=1179&ref=321 [nofollow] If you really are thinking about Alcatraz, make sure to book your trip before you leave. You never know how busy they will be.
And if it is a great spring day in the city, I know its seems a bit cheesy, but nothing beats sitting outside Fisherman's Wharf, enjoying fresh seafood with the amazing Bay Area sun and air. I have lived here my whole life and it is one of my favorite things to do still.
I am not sure how adventurous you are, but in the city I would suggest hitting up Asia SF. It is a riot and the food is really very good. Check out the website.
http://www.asiasf.com/ [nofollow] For whale watching, Monterey has some good tours. Im sure you can find them online.