More or less anywhere you are likely to find hotels and pubs with live Scottish music (and loads more with horrible musac). There are too many to list and anyway they keep changing what they do and when. There is no particular one that I am knowledgeable enough to recommend but there are a couple of festivals in September - one on Colonsay and the other on Jura. And Islay has a jazz festival, also in September, which sounds fun. Also there is the Islay Festival of Music and Malt in late May every year.
I imagine most boaties would not be wanting to go to the cinema unless the weather was really really horrible, and anyway there are very few to go to. The cinema in Oban has reopened after a massive fund raising effort. Tiree may still have a community cinema which is struggling, in Crossapol bay which is too far to walk from any of the anchorages.
I have never managed to catch the mobile Screen Machine, but it serves a very useful purpose indeed and surely should be supported. It travels on a truck around various locations in the Highlands and Islands including Tobermory and Gigha.
if you are into films you must also look at Scotland the Movie Location Guide which tells you were various scenes were set in the many movies which have used Scotland as the backdrop from the 39 Steps to Harry Potter to Braveheart and very recently Skyfall (that is the latest James Bond if you live on another planet).
I think there is only one theatre and it is wonderful - the Mull Theatre just out of Tobermory. Go there.
The Mendelssohn on Mull Music Festival happens in July and is worth catching if one of the venues is convenient for anchoring, like Duart Castle, Salen and Bunessan.
The Corran Halls in Oban, an unattractive 1960s flat roofed affair, has various visiting shows as well as conferences which you can track on their website.