Two well-known levadas are within 2-4 km from Quinta da Fajã.

"Levada dos Tornos" is approximately 2 km from Quinta da Fajã uphill on the road to Camacha. To the left the levada goes to Monte, to the right towards the village of Camacha. Also from there you can descend towards Quinta do Palheiro Ferreiro Gardens.

Two km further up the road just before Camacha on the road to Poiso is the “Levada da Serra do Faial" which to the left goes to Campo do Pomar and right to Santo da Serra.

Both can be accessed from the centre of Camacha.

See maps below from the book "Walking in Madeira" by Paddy Dillon

An even more recent book is "Walk! Madeira" by Shirley & Mike Whitehead 

There is a short description of "Levada dos Tornos" at walkmeguide.com

Holger is walking on Levada dos Tornos.  David took the photo from ER102 - 2 km from Quinta da Fajã.