Whereas it stretches a definition to call the walks from Monte a secret, they aren't obvious - and so much is obvious at Monte that you could easily miss them.
Leaving the main cable car [from Funchal] turn right to a square with a chourch and you will find the footpath signed near it.
There is a wonderful footpath to the little village of Curral dos Romeiros. There are steep slopes but no technical difficulty and you pass through some of the native forest. In late April the wild mimosa was well in bloom.
Two levadas are within range and signposted from this footpath. If you are staying in Funchal, you can return by bus from Curral dos Romeiros or, following the Levada dos Tornos, from one of the tea houses.