In reply to johnlc:
The peninsula sao lourenco
Is a must on a nice day. Fantastic coastal cliff scenery, quite exposed in one or two spots, but protected by cable fencing. The final peak is a steep hike up and down a heavily worn/eroded path.
Go early as it's one of the most popular routes on the island and can get crowded. Well serviced by buses to the start/finish.
http://www.theculturemap.com/peninsula-sao-lourenco-hike-madeira/
Good luck with your landing at the airport. We went in February this year with EasyJet, and due to high winds had to be diverted several times once back to Gatwick, once to a neighbouring island where we sat on the tarmac waiting in vain for the wind to ease, then diverted to Faro, and once to Lisbon where we had to stay overnight before finally succeeding in landing in a strong and frightening cross wind. It took us 4 days of attempts to get there, so we lost half our holiday. We have since learnt that Madeira is notorious for failed landing attempts being one of the most difficult airfields in Europe for landing - experiences like ours are quite common. If you do encounter delays, diversions etc. insist on getting proper receipts from taxis, hotels etc. EasyJet tell you that they will reimburse you, but they don't and we have had an ongoing fight with them to get reimbursed. They don't answer correspondence, their customer service is appalling and despite promises made on the flights and airports they do not honour them. We are getting nowhere with them. If any of their staff, particularly ground staff make any promises to you, get that person's name, and record everything.
Also be aware that you could meet similar problems going home if the outcoming aircraft can't land and you have given up your hotel accommodation - fortunately our return flight went ok.
Good luck! It's a fabulous island if you can get there!