Depends what you mean by 'close'. Your'e not giving much away Codhead. Scotland's big, It has a massive coastline, what are you after exactly? Are you looking for somewhere to stay on the coast with some fishing or are you looking for some fishing with somewhere to stay? Two different things.
Drummore & Portpatrick are on the Rhinns of Galloway, (& are MILES from Arbroath & on the opposite coast) so aren't too far apart but It's only a tiny part of Scotland.
Or is this a troll?
Do some Googling.