I've just spent close to two full days on Arran. I was lucky with the weather, with no rain at all and Blu skies for out of the time.
Anyone heading that way this month should be aware Brodick Castle is going to be closed on Thursdays and Fridays in May. It's apparently a staffing issue. I'm told the information is now somewhere on the website, but I didn't see it when I looked 3 days ago. My travel mate was extremely disappointed to miss the castle, though we were able to enjoy the lovely grounds, which have a lot of flowering bushes. There was no one collecting an entry fee as of yesterday.
Without a map to carry around, exploring the property was a bit challenging, but a couple of groundskeepers helped me find the charming Bavarian Summerhouse, which was what I was most looking forward to seeing. There was no food available, and I'd guess that should be expected on the days the castle is closed. I assume the toilets were locked, but I didn't check on that.
As previously reported on the forum, Arran has good bus service for an island, but--aside from the southern part of the island--buses are infrequent enough that a prudent car-less traveler will want to refer carefully to the schedules. Stagecoach runs the buses. I was unable to find printable schedules on its website, but my hotel (the Douglas in Brodick) kindly printed them for me. Quite a lot of the buses run only on school days, so ithe full, footnoted schedule must be consulted. The information below is just intended to give an idea of how well one can move around the island by bus.
There are three basic routes, all of which have at least some departures terminating at the village of Blackwaterfoot, directly across the island. Blackwaterfoot is therefore a good connecting point for those wanting to see as much of the island as possible by bus. There's a hotel at Blackwaterfoot with a full-service restaurant, a small sandwich shop, and a bakery that's good but seems to focus on bread products as opposed to sweets.. There are public toilets at the landward edge of the parking lot where the buses terminate.
Bus 322 runs approximately straight across the island, along "The String", to Blackwaterfoot, Machete Triangle or High Dogarie. The trip takes about 28 minutes. Mon-Fri departures from Brodick Ferry Terminal are at 0607, 0610, 0645, 0707, 0730, 0732, 0940, 1055, 1240, 1445, 1600, 1635 and 1925. Some of the early-morning buses do not go to Blackwaterfoot. Return buses depart Blackwaterfoot at 0725, 0822, 1010, 1255, 1504, 1536, 1540 (not on school days), 1825, 1955, 2035 and 2050.
Bus 323 is the most frequent. It runs around the southern part of the island, much of the time along the coast. It departs from Brodick Ferry Terminal at 0600, 0730, 0805, 0850, 1005, 1055, 1130, 1241, 1335, 1400, 1435, 1525, 1535 (non-school days), 1625 (Mon-Thu school days), 1635* (non-school days), 1645* (Mon-Thu school days), 1735, 1836, 1925*, 2015, 2115 and 2215. Only the asterisked departures go all the way to Blackwaterfoot. Return buses leave Blackwaterfoot at 0640, 0800, 0930, 1220, 1325, 1440, 1505 (non-school days) and 1757. Other return b7ses begin at Whiting Bay. The full trip between Brodick and Blackwaterfoot takes 70 minutes.
Bus 324 runs around the northern (more scenic) part of the island. It departs from Brodick Ferry Terminal at 0800, 1055, 1340, 1635, 1715 and 1925. The trip takes about 80 minutes. Return buses depart from Blackwaterfoot at 0917, 1207, 1446, 1735 and 1755 (non-school days).
Arran is attractive, but honestly, if you can't hike, don't want to hike or don't have time to hike, I think its charms are a bit subtle, given that reaching it involves a ferry (albeit quite an inexpensive one. YMMV.