Passing Prestwick, Ayr can be reached in roughly an hour by train. There's not much to be seen, not counting a nice beach walk and a ruin in the distance. Still, it's worth a visit. You should be able to bath in the sea. At least in the summer...
The trip costs about 7 £ and You'll be back in time for a pint or two.
Walking to the ruin is nice, but actually reaching it might be a little bit difficult.