We have the partial skeleton of a Minke whale down at the Field Centre. The Minke is probably commoner around Islay than a lot of people realise - and May/June/July is certainly the best time to see them.
If it is a reasonably calm day, the calmer the better, your chances of seeing one from the Caledonian MacBrayne ferry coming to Islay are very high indeed during those months - you simply have to sit out on deck and watch. Binoculars are handy - but not essential. I dont think I have ever systematically watched for sea mammals from the ferry on a good day in the summer and seen nothing - even if it is only a few porpoises.
Minkes are unmistakeable - they are usually 20-30 feet long with a slightly hooked dorsal fin. I once even saw one porpoiseing - repeatedly jumping completely clear of the water on ten separate occasions, one after the other. An amazing spectacle. That was off the north end of Gigha, which seems to an optimum place for some reason.
Another excellent whalewatching trip is the Colonsay ferry from Islay on Wednesdays - the north end of Jura is a real hotspot. I remember sitting on the cliffs above the Gulf of Corryvreckan eating my sandwiches, with a Minke whale slipping through the crystal clear water, really close to shore below me. A good day out.