We have just come back this weekend having looked and failed to find Cavalum tubes (Furnas do Cavalum), see https://pt.wikipedia.org/wiki/Furnas_do_Cavalum
. (Our primary reason for the trip was to look at the geology of the island.) We found a geocache web site at https://www.geocaching.com/geocache/GC3WR71_furnas-do-cavalum?guid=d5a2e882-e621-4829-bb2c-5efb4517c6e2
which gave one location with coordinates N32? 43.709' W16? 45.859'. That took us to a levada and a 'rock shelter' ? not a sign of flow, just possibly a steam explosion in a basalt flow over a blocky ash layer. We found a second 'rock shelter' just around the corner from the first. Neither looked anything like photos of tubes and environs provided in geocache web site and elsewhere which show low crawls. The land around this location was all cultivated and did not seem likely to have 4 tubes but we did not crawl over the land.
Our map indicated an information point in Machico but we failed to find it as we drove through the place. Perhaps the Funchal Natural History Museum might have a person able to answer the question though the translation might be a challenge.
Vincente tubes are just about worth a trip, thought why they had to put a dam in to create a lake mystified me, (possibly the reason was lost in translation.) The newish display center is worth going to (it came at the end of the tour) with a 3D film which was curious in parts.
I have heard a claim for some other tubes on the island but have no details. There is an expressed concern over damage to the environment of the tubes killing off cave adapted millipedes so perhaps there is a reluctance to publicise locations.
Another curiosity is the limestone quarry near by Vincente tubes at roughly N32? 47.834' W17? 01.360' with some good fossils but no caves! (Apparently it was a fossil coral bed lifted up at some stage by an eruption.)
Otherwise levadas provide good walking though far from level as one might think. Indeed the whole island is just one hillside at roughly 30 to 45 degrees. I would recommend the Rother Walking Guide for Madeira. Several have tunnels cut through hills which can be walked but a good torch and waterproofs are recommended. Strangely one also seems to spend a lot of time in road tunnels, some 3km long.
The claim is one can use buses but we found a hire car gave much more flexibility (though we also got stung for mileage charges - only 35km/day free which can't even get you to and from the airport).
PM me if you want more detail.