Ciao tourist,
The Boboli gardens are wonderful for seeing an Italian Renaissance garden in Florence. Its maintenance has improved greatly over the last few years and it is also huge! Since you'll be there with your tour - hoping you see all of it - I'd recommend you then head on to the nearby
Bardini garden. The entrance is through Costa San Giorgio, close to the Forte Belvedere. If the entrance/exit to the Boboli gardens near the fort is open, go through here.
NOTE: your cumulative ticket to the Boboli gardens and some of the Pitti Palace museums also let you into this garden so make sure to save your ticket and use it (valid for 3 days).
Another beautiful garden which you might be able to catch while it is open is the
Iris Garden located to the side of Piazzale Michelangelo. It is only open for a few weeks between April and May and is free entry. It is beautiful to see all of the varieties of irises in bloom!
Also open in May is the
Rose Garden below Piazzale Michelangelo. Entrance is through via di San Salvatore al Monte which is not really a street but stairs with the Via Crucis along the way. You get to it by going up from the San Miniato door along the old section of the wall that goes from the Forte Belvedere down the hill toward the river. (hope that made sense, check a map

!)
A final recommendation is the
Orto Botanico Giardino dei Semplici, or Florence's Botanical garden. From
this link, you'll see this garden also dates back to the 15th century and is one of the oldest in the world!
All of these gardens are in Florence and can be easily reached by walking or by bus. Hope the suggestions are useful for planning your visit in Florence, if you have any other questions don't hesitate to post them!