A Confeitaria (on Avenida do Infante) is a great place for a light lunch. You will probably be drawn in by the massive display of cakes that all look delicious. However, while the cakes were good, they were not as incredible as they looked.
What I did love though at A Confeitaria were the savoury options, pastel de nata and the drinks - the lemonade and the maracuja (passion fruit) tea. And since Madeira is all about the passion fruit, this is something you simply must try. We spent several pleasant afternoons reading there while sipping on the delicious maracuja tea. You can have it hot or iced as well.
And speaking of teas, Funchal Tea House (Loja do Cha on Rua do Sabao) has the most amazing selection of loose leaf teas.
You can sit at one of the small tables outside on the square and leisurely sip on something from their extensive tea menu (sweetened by some yummy cake perhaps...) - and if you like it, you can go inside the shop and buy some tea to take home with you. We stocked up on some delicious white tea - best white tea I have ever had!
The Ritz cafe in the old town of Funchal (on Avenida Arriaga) is a fine establishment with beautiful blue tiled wall mosaics. There is a lot of outside seating and you can choose to either look at the cafe building itself or the small park across the street.
The Ritz is one of the oldest cafes in Funchal (over a hundred years old, to be precise) and apart from the normal food and drinks also serves delicious homemade gelato. Well worth a visit!
Last but by no means least, for the chocolate lovers out there I can highly recommend Uaucacau (on Rua da Queimada de Baixo in the old town), an artisan chocolaterie where you can stock up on some truffles or chocolate covered nuts.
Uaucacau is a shop/cafe with a couple of tables as well, so you can sit down and relax with a cup of hot chocolate, which is absolutely amazing and served with a little chocolate spoon.