The best-kept secret about the Portland area is the county library cultural pass. Like most people, we love exploring touristy places but hate paying the entrance fees. Each county library system has their own list of museums/sights which you can check out a cultural pass to get in for free! Some passes are more popular than others so if you want a popular pass you have to reserve it ahead of time (more on that later). For the Japanese Gardens we just walked into the library the day we wanted to go and the pass was available : ) With or without a pass I think the Japanese Gardens deserve a visit. However, the admission price is $20/adult.
