Bar crawling in the Bairro Alto (but keep your wits about you - the area can be dangerous late at night), specifically Bar Lux.
Best African music club I found was to be had at Luanda Bar, and B-Leza is worthe checking for live (mainly Cape Verdian) music (which will probably not sound as you would expect - as usual what we get presented with here from Cape Verde is very different from what is popular in Cape Verde). In general, African music in Portugal is derived from ex-Portuguese colonies, and has a different flavour to most of the African music that we hear in the UK.
If you find that you like this music, take a trip to Sons D'Africa to buy some CDs that you'll never find in Britain.
For fado just wander round Alfama in the evening and listen to what's coming out of doorways.