The Glass floored cliff thingy at - Miradouro do Cabo Giräo
A day Taxi tour is well worth it (although expensive), the driver will offer several tours, get a driver who speaks a language you understand.
Day trip (via ferry) to Porto Santo island (have a jeep trip whilst there). Ferry goes out about 8.00 comes back about 6.00 two hours each way.
Blandy's is interesting (take a flash gun).
Tropical Gardens via the cable car.
There are loads of glass bottomed boats/trimarans/galleons etc sailing from the harbour
Open topped bus hop on and off day tickets, local to Funchal.
Câmara de Lobos - the open topped bus stops here, this is where Churchill came to paint.
Fish (and fruit) market, Funchal
Beware Funchal front is being radically redeveloped at the moment (extending moorings for cruise ships and extending the harbour) so a lot of it is dug up and/or screened by corrugated sheeting.
The old town is quaint but you do get mobbed by restaurateurs, but they are all friendly.
Restaurants -
Armazem Do Sal
Restaurante Dos Combatentes
Try
Scabbard fish and banana
Beef on a stick - espetada
acorda - soup with a poached egg in it
prego no prato - Portuguese beefburger