I have been a couple of times, and would say, book a car if only for a couple of days (do it locally for a good price) and drive over the whole island - you can do the right hand side to the top coming back right the way down the middle on one day, and the other side the next. Lots of fantastic scenery, more mountainous than you would think, and very enjoyable.
Try the Espada, which is the local fish, very nice indeed. Don't forget the local wines either, you can have tasters of the madeira wine, and the madeira cake there is not the same as the one available here.
Go up to the top of the cable car, where the botanical gardens are, and spend some time there, wandering around the plants. It is cooler there as well, so if the weather is a bit warm in Funchal, then that is the time to go.
Have a good time.