It all depends what you consider best. If you want smaller or low key bars, then try Bairro Alto
If you want large, expensive lounge bars and dance clubs, then most are located down by the river on Avenida 24 de Julho and around the docks below 25 de Abril Bridge.
Alcantara docks around by the bridge, and also some quite upscale ones on the waterfront in the Parque de Nacoes.
Cheers thats enough info to get me started !
Chiado, Alcantara (around the docks) and also the Barrio Alto.
Don't forget the Alfama district.