Perhaps the most stunning hidden spot of Madeira is Achadas da Cruz. It's located on the far west coast of the island just a 20 minute drive from Porto Moniz. This is the furthest away from Funchal you can get, but well worth it.
You can park right next to the cable car, which is Europe's steepest with a 98% incline. If you are afraid of heights, you might not be up for it, but see if you can overcome the fear and you will be happy you did. Because it's not just the cable car ride you come for. It's the castaway promenade where you walk in what looks like an abandoned, medieval village. No one lives here, but it's still used for agricultaral purposes. During summer there is a little bar, but it's not always open. It depends on whether or not the owner has been able to find staff. Either way, you come to go for a short walk and just enjoy the raw nature and endless oceans that goes uninterrupted all the way to North and South America.
If you are up for it, you can bring the essentials for a nice little picnic. We once camped here and it was amazing.