Islay, "Queen of the Hebrides" is around 20 miles by 20 miles. With its nine distilleries - Bunnahabhain, Bruichladdich, Bowmore, Caol Ila, Ardbeg, Laphroaig, Port Ellen (closed), Lagavulin and the relatively new Kilchoman distillery - it is easy to see why Islay is probably most famous for its whisky.
The Isle of Jura, five minutes ferry ride from Port Askaig. (Note that the ferry terminal on Jura is 8 miles from the main village and that public transport only meets certain ferries by arrangement.
The Isle of Colonsay.
The Islay has two ferry ports Port Ellen and Port Askaig, the ferry journey is a 1 hour 40 mins trip from the mainland, it leaves from Kennacraig, near Tarbert (Loch Fyne) on the Mull of Kintyre, which is about 2 and half hours from Glasgow by car. Caledonian MacBrayne operate the ferrys and Citylink coaches connect with some ferries at Kennacraig. There are two or more trips per day, with more ferries going to Port Ellen than Port Askaig.
British Airways also runs two return flights per day between Glasgow international airport and Islay airport.
Take a distillery tour. Even if you don't like whisky it's really interesting to learn about the distilling process and see how the distilleries have shaped island life. If you do like whisky you generally get a free taster. The main tours are available at Bowmore and Ardbeg distilleries where there are visitors centres and dedicate tour guides, though it may be possible to tour other distilleries by appointment.
Use the swimming pool, sauna and gym at the McTaggart leisure centre in Bowmore.
You can sit on the beach at The Oa, and watch as Highland cow stroll past
The cafe at Ardbeg distillery is wonderfully rustic with some great menu choices including good soups and home baking.
There is a good Indian restaurant in the center of Bowmore.
Islay is a pretty safe place and any crime here is likely to be big news.