Just spent a wonderful week in Madeira and dined in Restuarante a Bica on every night except Sunday - closed - simple local Madeiran dishes cooked beautifully and served with care. Waiters all speak most european languages well - French, German, English, Portuguese, Spanish - many a pleasant hour sat chatting to the owners who love to do the same.
Prices were cheap, considering the value - typical cost of 3 course meal consisting of - garlic bread, wonderful soup, main course of fish / meat with fresh vegetables, bottled water was 25 euros. They also make their own icecreams - well, well worth a try.
They are based on the Rua do Hospital Velho, to the left side of the old food market as you face it at the east end of the promenade.
If you prize good home-made cooking and a friendly atmosphere then this is good.
They also serve lunche time meals but we didnt try them.