Isle of Arran - 'Scotland in Miniature' as the tourist board says. Scenery, castles, arts and crafts, local food, ales, whisky etc etc.
When we were living in Ayrshire for a couple of years, it was our go-to destination for cycling and walking. The roads are quiet, plenty of varied scenery - mountains, lower hills and gentle coastal pasture on the west side. Mrs T did her first YH trip there on a 3 speed shopper, luggage in the front basket. Goat Fell is a good climb with great views of surrounding peaks and distant lowland Ayrshire.
Ayrshire CTC had a ride there every year, when the plan was to get the first ferry, circumnavigate the island on the fairly benign coast road and be back in time for the boat back to Ardrossan. Never achieved, as we spent too long in the pub at lunchtime. The 'String Road' through the middle is the only big climb with a cracking straight-ish descent [going W to E] where you might top 50mph ...
If the weather is bad, it's easy to hop over to the opposite, sheltered coast and plenty of indoor touristy things to do if it's really foul. The very mild climate means summer flowers will still be in full bloom in October.