This has clearly been a superb horticultural and arboricultural resource, carefully laid out with education in mind (it is part of the university). Alas it is a little bit neglected, probably due to lack of finance. When we were there a long spell of drought was affecting even the hardiest plants. Nevertheless well worth a visit - on the blistering hot day we were there the shade of the trees was most welcome. Plenty to see and most of the plants are well labelled.
It is very central, being located just to the west of Av. da Liberdade on the edge of the hill. We had a bit of difficulty finding our way into it, having walked up from our hotel via Rua da Alegria where we found a fine old stone gateway carved with the lettering "Jardim Botanico da Universidade de Lisboa" but this had large rusty iron gates firmly chained and padlocked shut. This had clearly once been the main entrance and we could see the garden beyond. We carried on round the maze of streets to climb the hill and found the modern entrance halfway along Rua Da Escola Politecnica with a smart new ticket office. Entrance only cost us €1 each at concession rate - excellent value. This included a helpful map of the layout.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.