The university botanical garden is a quiet escape from the city's traffic and noise, occupying a compact plot near the cathedral. It was founded in the 19th century and maintains a collection focused on Mediterranean flora, including species native to Sicily and southern Italy, along with succulents, subtropical plants, and a modest but well-curated collection of economically important plants. The lemon trees are particularly fine — this is lemon country, after all, and the university takes the collection seriously.
It's not a large garden and won't occupy you for more than an hour, but it's a pleasant place to spend that hour, especially on a hot afternoon when the shade and greenery offer a genuine respite. The garden is affiliated with the university's faculty of sciences and occasionally hosts academic events. Entry is free or very cheap, and it's rarely crowded. Worth combining with a visit to the cathedral and the Annunziata dei Catalani, both a short walk away.