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!
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.
Even if you don't have the opportunity to actually visit, the sheer amount of publicity you get from its exterior is incredible!