You must distinguish between street fado and professional fado.
I always prefer the street fado try Tasca do Chico (Bairro Alto and also Alfama)
A Tasca do Chico (Bairro Alto)
Rua do Diário de Notícias, 39
Tf. 21 343 10 40
Check also the http://www.museudofado.pt/ about 6 years ago