SF has most of the attractions that major cities have.
There is a gay film festival for the last 10 days of June. Plus a gay pride parade and lots of gay events the last weekend of June.
What Mikew said about the weather is true, but in the summer it can be hot as well as cold - on the same day. In the summer it can be 98 degrees and still one day, and 60-65 degrees and foggy with a 20 mph wind the next day. And even when it is cold in SF, 15 miles outside the city, it can be in the 80's and 90's, so bring appropriate clothing - a light jacket is a necessity.
If you want to go anywhere outside of SF or Oakland, you need to rent a car. OTOH, having a car in the city is a major liability - parking is limited or expensive. There are major wine vineyard regions north of SF - Sonoma and Napa counties. Yosemite Park is worth a drive - but is probably a 2-day trip.