Alcatraz & the Golden Gate Bridge are definitely worth it...In July it will be cold, so bring layers of clothing. Here is a local's opinion of what you can do...If you want to use public transportation, use www.511.org to plan out your trip.
Start at the Ferry Plaza. You can walk from there down the Embarcadero to Fisherman's Wharf. From Fisherman's Wharf take a ferry out to Alcatraz, it is awesome. Check out Ghiradelli Square and North Beach...you can also wander into Chinatown from there. If you stay on the Embarcadero, you'll go past aquatic park and into Fort Mason. That'll lead you to Chrissy Field and some breathtaking views of the Golden Gate Bridge. You can walk down to the base of the GGB, it is flat and probably about 3 miles along the shoreline.
Then head up to Nob Hill. Marvel at Grace Cathedral, it is really quite majestic up at the top of the hill. Check out some of the super swank society up there. Go up to the Top of the Mark and check out the entire city. Walk down Sacramento Street to Polk, hang a right, and head up Polk into Russian Hill. Cute shops, nice homes if you wander through the hills. When you get to Union Street, go left and down the hill into Cow Hollow. Walk down Union Street-- lots of good shops and restaurants-- and you can walk to cab it over to the Palace of Fine Arts. Awesome. The Presidio is right near there and is also a cool place to check out.
Then go up and over the Fillmore Hill. At the top, you will see a beautiful view of the Bay. Head down the hill into Lower Pac Heights. Japantown is also right around there. If you continue down Fillmore, you'll hit the Jazz and Blues area. Cool old clubs, the Boom Boom Room, etc.
Go down Geary St...if you get off the bus on around 2nd street and go right, you'll hit Clement Street. It is little Chinatown, and has some cool shops and restaurants. Go back to Geary and take the bus down to the Cliff House and Ocean Beach. Check out the Sutro Baths. Walk through Fort Milley to Land's End and back-- spectacular views of the Marin Headlands. Continue down on Ocean Beach and have a drink at the Beach Chalet. (you can continue down the Great Highway to the SF Zoo, which is supposed to be nice, I haven't been in a long time, but in my mind one of the few things to check out in the outer sunset)
The Beach Chalet also marks the end of Golden Gate Park. You'll see some windmills. You can work your way back through the park, I believe it is about 3 miles long in total...lots of little things to explore, and the new deYoung museum is there. Supposed to be great. The Tea Gardens are right there, as well as the other gardens that I am totally blanking on but is cool to check out.
Exit GGP on 9th Ave and head up to Irving. Another cool little area in the inner sunset. Get on the N Judah and get off on around Masonic. Head down a block or two onto the Haight. I personally don't like the Haight-- there are a bunch of rich brats living out their homeless fantasies and begging me for money-- it is a must see. Wander around the upper Haight, past the Gap on the corner of Haight & Ashbury. Have dinner at Cha Cha Cha. Or there are some fantastic mediterranean places down there. Eat breakfast at the Pork Store. Walk down to the Lower Haight, a little seedier but still and interesting area. Have a drink and catch a soccer match at Mad Dog in the Fog. Hang a right on Divisidero and head down to the Castro.
Walk up and down the streets in the Castro. Fun area...Market Street has lots of interesting stuff as do the surrounding streets. Catch a bite at Nirvana. People watch for a while. Go to Market & Church Street, get on the J-Church line, and head over to Noe Valley. Get off the bus at 24th & Church, and wander around Noe. Get a feel for the neighborhood, because soon you'll go to the Mission, a nice contrast.
After exploring Noe, and getting maybe a burger at Barneys, head back to the J line. Take it to 17th Street. Take a nap at Dolores Park, and check out the Mission Dolores next door. GREAT people watching. Dolores Street has some great homes, but it is time for you to head to the Mission.
Head down 17th street. You can check out Guerrero, but there isn't much there; you want to hit Valencia and Mission Sts. Valencia and 16th starts a few blocks of hip bars, hip eateries, and hip shopping. Delicious burgers can be had at Big Mouth Burger on 24th at Valencia. Yummy Spanish food at Picaro, 16th at Valencia, and Ti Couz is pretty popular, also 16th at Valencia. Blondies is good for dancing, Casanova good for drinking. There are tons of places in this area. And if you head over to Mission Street, you will be hit with a barrage of some of the best Mexican food you will ever have. Be careful around the Mission, but definitely check it out. There are also tons of murals painted on buildings if you walk around a bit. Spend some time there, it is a part of the city so vibrant yet often neglected.
Walk down to Folsom Street and get on the 12 Folsom to head up to SOMA. Get off at 3rd/Folsom, go left, and you'll see Yerba Buena Gardens and the MoMA. There are also lots of restaurants and clubs in SOMA (South of Market). The Metreon is down there, if you are in the mood for a movie or some arcade games. Head up to Market Street. This is a big tourist section and where you'll find the cable cars. Walk around for a while, head up to Union Square. Go down Maiden Lane for some little boutiques. Go to 5th & Market and watch the chess games and check out street vendor's wares. Take the Cable Car back up to the top of the hill, or back down to Fisherman's Wharf.
One part I left out...Twin Peaks. On a clear day the view up there is amazing (on a foggy day, well, it is cold and miserable up there). To get there, you take Market Street all the way through the Castro and up the hill. Make a right at the top to go up a little higher.