@japes has covered most of them.
Would recommend St. Luke’s, is a converted church venue space/bar. There’s a couple of things on this week, including the sugar hill gang on friday.
http://www.kingtuts.co.uk/whats-on#/june-2017 has stuff on most nights.
Bars that japes hasn’t mentioned:
Central - shilling brewing co, hippo taproom, saramago at the cca, yesbar
West - hug & pint, Inn deep, six degrees north, grunting growler, West on the corner
South - clockwork brewing.
Also, there’s a few events of this left http://www.westendfestival.co.uk/events/