The jardin botanique de la Villa Thuret is a good free attraction, particulary when your interest is trees - especially from the southern hemisphere. It's located on the grounds of the Villa Thuret, in Cap d'Antibes.
The entrance to the garden is available from the Chemin Raymond street (A; GPS: 43.563136, 7.125045) which is a narrow street connected to the Boulevard du Cap. There are a few places for cars on this street (P1; GPS: 43.563242, 7.125438) but much better is to park in the larger layby just on the Boulevard du Cap (P2; GPS: 43.563802, 7.125619).
The garden was founded by botanist Gustav Thuret in 1857. In the garden there is a large collection (about 2,500) of trees and shrubs (1600 species) growing in warmer climates and coming from both southern Europe and the Far East. These include some eucalyptus trees and huge palm trees, as well as several varieties of oaks. Nearby the villa there is a monument of the founder.
The place looks a little wild, and additionally seems to be a little neglected (maybe that's what it should be), which however, on the other hand, adds to it some charm. Don't worry - apart from the sightseeing just take something to eat, sit down on the grass near the villa and enjoy the beautiful views through the surrounding trees on the distant Alps!