Welcome to California!! I really hope you enjoy yourself here, though I know that leaving your old life behind is probably very difficult.
I would recommend a day or weekend trip up to gold country, also known as the motherlode. It consists of the foothill region, going down Highway 49 from around Nevada City to Sonora. There are several small towns that have kept up their historic districts, with great little shops, museums, and gold panning in some places. The Empire Mine in Grass Valley is a nice little place to visit, and there is an Indian casino in Jackson that my boyfriend and I enjoy going to every once in a while. There are also some underground mining caverns that you can take tours through on this route, as well as several awesome vineyards. All of this is about 3 hours east of the Bay Area, which is why I suggested a weekend trip if you are really interested in any of this stuff.
In the actual Bay Area, I always enjoy a visit to the Winchester Mystery House. And I'm actually planning on meeting up with some family and taking a ferry into the city to hang out at Fisherman's Wharf soon. I would suggest visiting the Oakland Zoo, as it is my favorite zoo to go to. I'm not exactly sure why, it isn't the biggest one I've been to, but I just really like the atmosphere and way the exhibits look. There is lots of open space for many of the animals to roam in. And they have a sky thing (I cannot remember the term for it right now) where you ride in those buckets in the sky...you get a really awesome view of the bay from up there, and you get to look down on animals.
I would also suggest Mount Diablo State Park, Santa Cruz beach boardwalk, Old Sacramento, Golden Gate Park, seeing a play in the city if that's your thing, and going to Six Flags Discovery Kingdom if you are into theme parks. It is half zoo and half thrill rides, I've been going there practically since I was born so I may be biased, but I think it is a fun place to hang out (try to get discount tickets somewhere though, otherwise it gets expensive).
I'm sure there is tons more that I am not thinking of, but my mind is going blank at the moment. I'm sure you will find lots of stuff to do around here. Have fun!
If you mean that it's hot, it really hasn't even been as hot as usual lately, and San Jose is actually quite nice compared to the temps a little to the east of you.
