We stayed in Brodick, really nice self-catering place overlooking the bay; far enough up the hill to be away from the noise, close enough to walk into town.
I’ve only done road riding round there (both ways), I preferred anti-clockwise. The road across the middle of the island is beautiful too, do it so you finish in Brodick. Superb descent. Loop round the island is about 60 miles, nice 4hrs or so at a steady pace.
Arran Cycling Club website:
http://www.arranbikeclub.com/
Touristy stuff – Brodick Castle is worth a visit, there’s a whisky distillery in the north of the island (Lochranza) and somewhere on that middle road (nr Machrie IIRC) is a big visitor centre with arts & crafts, helicopter flights over the island etc. Lots of wildlife to see, beaches to sit on, plenty of ruins and Bronze Age stone circles/burial sites.