I greatly enjoyed the Boboli gardens in April because I was bird and butterfly watching. (and lizard watching) There are some zig zag trails to wander through the wooded area. There is a large "duck pond" with an island in the middle. In April visitors could not go out onto the island, they could only walk around the pond or sit in the shade on a bench near it. There is a very long building called the Lemon House which was full of potted lemon and orange trees in April. They may now be out in the grounds.
I noticed many people though were just power walking through and they did not look too happy. They were on the two main wide trails/roads that allow a person or vehicle to get through the grounds in the minimum amount of time.
The park is large and it did not seem that flowering plants were a major feature. Some minor trails were taped off while they removed damaged trees.
If nature watching or sitting in the shade enjoying a beautiful day sound appealing, I recommend the Boboli. If that does not sound appealing, you may want to check online further to make sure it offers what you are looking for.
We took the bus to the Porta Romana and walked back towards the Pitti. (Either way there will be some up hill sections.) Be aware if you do not exit near the Lemon House, you may have to walk a very long arc around Pitti, down, through the back of the property and in through the courtyard to go out through the main Pitti entrance. Hopefully they have opened another exit route by now, but that was the route in April and it was frankly a bit of a time and energy waster.
Admission to the Boboli gardens is not free. One visit, security also was checking the contents of bags being brought into the park.