How is parking in Stanford? Will I find a spot near attractions like parks and restaurants?

Yes, you should be able to find a spot when you go to that sort of place, but as a general warning, there aren't a lot of restaurants or other local businesses here -- some, not a lot. These locations all have parking lots. Street-side parking just doesn't exist here, at least not that I've ever seen it. There are too few people living here for parking to be a problem.