I'd like to visit the "Parque Florestal de Monsanto" in Lisbon. But this is a very big (10 km2) park and I'm not not sure what area of the park to head to. Is there any area in the park in particular that is interesting to visit?
I suggest you start with the "Centro de Interpretação de Monsanto " (Monsanto Interpretation Center). It is a building with a lot of information about this area (pictures of flora and fauna, maps, guides...) and from there you can decide where you want to go next.
Unfortunately, this page is not translated, but you can try to use an automatic translater: http://www.cm-lisboa.pt/en/living-in/environment/monsanto-forest-park/espaco-monsanto From this page you can also grab more ideas.
Public transportations in Monsanto are not good. Bike is a very good option (generally speaking of course).