Orti di Parnaso reminds me just a little bit of Parc Güell in Barcelona. I am aware that this comparison is not fair to the Catalans, but when you go, you will see what I mean. First of all the park is located high above the city, which means that there is a lovely view over the before mentioned Giardino dell'Orticoltura but also towards the Duomo and Florence itself. From the top of the park and down along a large stairway is a gigantic colorful dragon perfectly made with a little fountain inside its big and wide open mouth. Very Gaudì'ish.
If you take the walk from befind the big tiepidarium in Giardino dell'Orticoltura you can walk through the park along the path which leads you up to the viewpoint, where you find several benches and a little fountain. Several lawns overlooking Florence and the park beneath are perfect for relaxing and sunbathing and are indeed occupied by lots of young people when the weather is right.
Entrance from Via Bolognese through Giardino dell'Orticoltura and from Via Trento.