I would double check with the rental place but I believe they are permited on all city streets. Renting a bike is another way to go and the ride from Aquatic Park to the bridge is all on a path so you don't need to worry about traffic.
WE rented one this summer. I think it was $70 for an hour or so. You are basically riding a go cart.Your helmeted head reaches about the height of a tire on an SUV. YOu are that low to the ground. There is no reverse, only forward. You can go anywhere on the street but you have to follow a map that shows you where to go. You can even go over the GOlden Gate, which I think would be crazy!! It is GPS oriented, but we somehow didn't follow the directions right, and the GPS shuts off until you find your way back. Imagine being in the little go-cart in Union Square and lost!! It was crazy, but the memory of that little go car will always be a funny memory!!
I don't know a whole lot about them, however, I do think there are better ways to explore San Francisco, rather than on these things --especially given the cost of renting them.
I see them all over the city. People seem to really enjoy them. I don't think they would be too great in the rain, or on wet streets though. They also don't offer a whole lot of protection in case of accident.