I‘ve happened to visit Madeira for a week earlier this year. While the weather was windy and very unstable, it did not stop me from exploring the historic, art, and food highlights of Funchal as I stayed in a nice apartment in the heart of the old town.
Public transport is not great; however, if you understand how it works, you can get pretty much everywhere with a bus. Just plan ahead.
I tried my luck renting an apartment on Airbnb. Please mind the street noise might be high at night if you want to stay in the town. Funchal and Madeira in general are very hilly. A 500m road on the map can take you 20 minutes to climb and leave you out of breath. Even if the property is close to the coast, it can be on a rock with no access to the ocean.
I've tried multiple times the local Black Scabbard-fish. Normally served with a grilled banana or passion fruit sauce. This dish will taste from normal to delicious depending on the restaurant. Pátio Das Babosas and Mozart are exceptionally good despite being in the touristic place. Another food discovery of the trip: delicious mango-falafel wrap and blueberry cake in Fala Fala
I can't stop recommending PR 8 hiking trail. You'll see some pictures below. To explore the city - book your free (based on donations) walking tour. Lisa was a great guide. When the weather is not favorable you can spend some time in a Arttia pottery studio making your very own vase or cup. As for the museums - Museum of Frederico de Freitas will welcome you as a home and surprise as a treasury chest.
Madeira has some many more things to offer.
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