Included in the ticket price for the Boboli Gardens are the Bardini Gardens. If I hadn't been told about them I don't think I would have made the effort to find them.
They are lovely gardens with a really good coffee house where you can sit on the terrace and look down over the Arno. So peaceful and relaxing with very friendly staff.
To find them you leave the Boboli at the exit near the fort, walk down a street, round a few bends, and then you find the entrance. It is signposted but you do feel a little unsure you are going the right way at first.
Make the effort – you won't regret it.