Madeira

It's a stunningly beautiful island, but both my trips were for 5 nights, I think. There's no way I'd get on a plane to go anywhere for just one night. Madeira's worth a lot more time than that. The airport's hair-raising, too.

You should think more about your exact itinerary for 10 days. Madeira is not exactly a "must", but we had an interesting three nights there. It's kind of a historical resort whose time has passed. It's a bit locked in amber, despite current interest in eco-hiking like the famous llevada trails there.

Transportation without a car can be an issue. Note that it is a rock island. The big resort hotels typically have a large seawater pool with a view of the ocean. But there may actually be zero sand beaches with ocean water lapping the sand. (Not sure.) We were not sorry we went, but you have other places in Portugal that are more important, like Coimbra or some Roman relics or Guimares or ... Indeed, we flew to Madeira from Porto, and back to Lisbon for a day or two before we flew home.

I believe Madeira has one very small, man-made sandy beach

I think Madeira is worth doing, having been there several times on day cruise calls, but would question flying in for a one night stay. It needs more time than that, and to see the island properly and effectively I think you need a rental car. The buses are timetabled around local needs.
I think the time is better spent in mainland Portugal.

Madeira is worth visiting but not for one night. You will spend too much time waiting in airports and in transit to really see anything. Spend the extra night in mainland Portugal as there is so much to see there.

Hello from Wisconsin,
Listen to Laura.

Madeira, what a great place for 5, 6 or even 7 days. One day, no. Oh, and to encourage you not to go, have you checked the airport on the island? Some say it is one of the most difficult landing sites out there. If I recall, the landing strip is sandwiched between a cliff and the ocean. And if you have never been intentionally sprayed with bug killer here is that opportunity, too.

We had a great time on the island. And their method of cooking chicken and beef over open flames makes for fine eating.
When you look at each other and say, "This is the best (fill in the lank) I have ever had." They raise the beef on the island.

wayne iNWI

We just went to Madeira in April after staying in Lisbon and Porto. It was wonderful and a highlight of our time visiting Portugal. We flew from Porto but all the flights left later in the evening so we got in very late to Madeira. We stayed for 3 nights and then went on to the Azores. In hindsight we should have skipped the Azores and stayed longer in Madeira. There is a lot to see and do there especially for those who enjoy outdoor activities. We stayed at the Cliff Bay Resort which was lovely and right on the water.

I think if you are only visiting Lisbon tacking on a couple night stay to visit Madeira is worthwhile. A one night stay is not worth the trouble though.