The house is beautiful, historic, and immaculately cared for. The front garden is a delight, and the view of Goatfell and the ocean is fantastic. Allan's a great cook and breakfasts were delicious and plentiful --- I don't think I managed to finish one, and not for lack of trying!
From Belvedere, you can walk down the hill to Fishernan's walk and take it all the way to Brodick castle and gardens, which can occupy an entire day. Walk uphill instead and find the (well hidden) start of the Coastal Walk through the forest and to the next village, Lamlash, another good day's activity.
Stop by the Brodick Visitor's Center near the ferry and ask for a map of the Coastal Walk, which extends around the entire island. And stop by Crofter's for dinner at least once while you're visiting Arran.