The world expert on great cumbrae will be along in a minute. There is a bike shop on the island where you can hire bikes? The island is basically the town of Millport and a road around the island and a road over the top which is not too high. There is a little cafe the ritz, almost back at Millport at fintry bay if you go round anti-clockwise, near the Indian rock ( a cliff that looks a little like a Native American). There is also the crocodile rock, highlight. Joke shop, cafe we used to go to at night as kids on our own as the place has little traffic. There is a cathedral which I think you can stay in, I am guessing a youth hostel, lots of private holiday cottages, the George hotel. The ferry from Largs goes to a slipway a few miles from the town, regular bus, or easy cycle. Co-op, butchers, tennis court, golf course, lion rock, newer cafe stop nearer the ferry slip. Eleven miles round. More cars now alas than there used to be.
All of this info is from the year and indeed the day elvis died. However as it is the 1950s on great cumbrae it should still be up to date.
The Waverley paddle steamer sometimes gets you there from Glasgow. If it is running you can also get on at Millport and go elsewhere on the Clyde e.g bute or around ailsa craig There used to be a boat that docked at the pier in Millport too but that might have stopped.
There might be Sustrans route all the way to Largs from Edinburgh but there is a very steep hill down into Largs, the hailey brae. Nardinis in Largs is restored to glory.
You used to be able to book fishing trips, the skipper gave you a hand line but the big Ruskie factory ships have taken much of the cod.
Bowling club used to do weekly membership. Again this was 1978. Bound to be many Nick nack shops. Kayaking might be option. You can also maybe stay at the marine research place. Glasgow uni psych dept field trip always went there.
Garrison gardens is a nice park. Recently spruced up. The hut theatre/cinema might be gone.
The pancake place long gone.