Pop into the RSPB at Loch Gruinart, they used to keep a list of recent sightings. At least there will be someone who will know what is around. They also do, or did when I was there, guided walks each week which will give a good insight into the reserve workings and the birds.
The road on either side of Loch Gruinart can be productive for raptors, buzzard, merlin, hen harrier. Also good for chough, but, Ardnave as previously noted should have a flock of them. I've had excellent views of otter in Loch Indaal, there is a spit going out into the loch near the end of the road from Kilchoman. Also have had them in the bays on the Atlantic side of the Rhinns. Purple sands at Bruichladdich and excellent whisky! Scoter in Loch Indaal. Golden eagles anywhere, plenty of barn owls. Especially good on the fence post across the flats at Gruinart. Swans on Loch Gorm. Waders on Loch Gruinart. Golden eagles from the hide at Loch Gruinart over the hills towards Jura.
Malcolm Ogilvie has a good book on the Birds of islay which details sites as well. Roy's in Bowmore will have it, or, the Natural History Centre in Port Charlotte.
There are so many places, you will have an excellent time, wonderful birding. I lived there for 4 years and still miss it.
PM me if you want more info.
Phil