Never stayed in the hotel but I come from around that area. There's quite a lot to do for non-golfers (I don't play golf) and I reckon it's an often overlooked area of Scotland. It's obviously not the Highlands but there are some lovely bays and gentle, pretty scenery.

In terms of places to go then Ayr, Alloway and Burns Country are close by. Also Culzean Castle which is a major Scottish castle with extensive grounds. And Glasgow isn't that far away for a shopping and museums trip.

Think the hotel has a good spa too which might be of interest.

(And this post having overlapped with the one above - which posted while I was typing! - you should be aware that Ayr is far from being a city.)