The "problem" with most live music n Goa is that it isn't live. Most singers, and many bands, use pre-recorded backing tracks.
A very good place for "proper" live music is Cavala in Baga, on Wednesdays (Bell Bottoms - mosly rock) and Fridays (Music Company - mostly retro).
Claudiine and Jimmy play at Molly Malone's on Tuesday nights (Monday next week on account of St Patricks Day).
Mayonna's is usally good on a Sunday - get there early as it gets very busy.
As others have said, Jazz Corner is also making a real effort to put on good music this season.
Of course both of the Saturday night markets have music - most people find that Ingo's is the better market, but Mackie's often has better music (and a much less irritating "compere")