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 music festivals on Colonsay, Tiree, Mull and Jura. And Islay has a jazz festival in September which sounds fun. And there is the Islay Festival of Music and Malt in late May every year. As festivals are all the rage for pulling in the tourists I imagine there will be more and more as the years go by.
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 Phoenix cinema in Oban is now closed for good, but The Highland Cinema in Fort William is doing well. I have only once managed to catch the mobile Screen Machine. Since 1998 it has served a very useful purpose indeed, and surely should be supported, because it travels on a truck around various locations in the Highlands and Islands including Tobermory and Gigha. It's the only full time self-contained mobile cinema in the UK.
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 the autumn and is worth catching if one of the venues is convenient for anchoring.
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.