The website states that tours are available "on days designated by the museum," so it seems you have to call ahead rather than just showing up on a whim. I've been there several times, but I've never been able to tour on a day when the museum was closed.
However, there seem to be other companies on the premises besides Ito En, so you can stroll around. There was even a bottlebrush tree on the grounds.
It's a really fun place where you can have all sorts of experiences, such as tea harvesting, tea making, matcha experiences, and tea ceremonies!
I was surprised to see so many different tea leaves grown all over Japan!
Located close to the nearest station, it's like an oasis in the city where you can enjoy tea picking in casual clothes. (^o^)
I highly recommend the matcha experience!
They teach you how to carefully grind the tea leaves with a stone mill, and afterwards you can enjoy the tea exhibits. I was very satisfied.