Golden Gate Park is huge. It's easy to feel like you're the only people on the planet as you walk around the more secluded areas (at least, during my visit, which was heading into the winter it was). I can't attest to what it's like in the summertime. I'm sure it's much busier, but with such a large area if you're looking for somewhere isolated I'm sure you'll find it.
In the park there are lots of things that you can do and see, but you have to pay extra for most of them I'm afraid. There's a Japanese Tea Garden which looked lovely from the sneaky photo I took at the entrance but I didn't shell out the money to go inside. I probably should have, but I felt like it was a good idea to save a few things for another visit in the future too.
I didn't go in the California Academy of Sciences either, because it is pretty pricey, and, while I actually think it would be worth it, I wanted to enjoy the rest of the sunshine while I could after our visit to the de Young Museum which was very enjoyable. There are lots of other attractions in the park too. Visit this page for information on others.
For most of the rest of the time there we just wandered and enjoyed breathing in the fresh air. We laughed as we saw a dog-walker with about twelve dogs on leashes go passed, disciplining them and somehow managing to keep them all in control.
I kept thinking of Yogi Bear for some reason as we walked passed huge open grassed areas with picnic tables. We had already eaten the lunch we'd brought with us before we reached these areas otherwise we would have definitely made use of one of them.
As we wandered I heard the whizzing of something flying through the air at speed, and then the dinging of something striking metal. I had no idea what it was until I looked closer and spotted targets for people who take frisbee seriously (there are quite a few of these people who visit the park). They stand far back and try to slot their frisbees between metal bars.
During our wander we also saw some ducks and other birds enjoying a swim at one of the waterholes. There were some small ones with dark feathers and compact little bodies that I don't think I'd ever seen anywhere else before.
The trees that grow in the park are huge. It's really nice to just walk around and enjoy the feeling of being so small compared to them. You could definitely enjoy some philosophical moments during your visit if you let your mind wander.
I enjoyed my visit to the park. It's a little out of the city but you can get there using public transport. If you take MUNI you can also show your transfer for a discounted admission to some of the places in the park which is a nice little bonus. If you decide to visit though, be sure to watch out for the Stow Lake Ghost.