In the coastal town of Lime Regis in West Dorset, England. There's a harbor wall known as the Cobb which factors heavily into the plot. And they go to this town because Wentworth has friends Captain Harville and Captain Benwick. While they're there, William Elliot is also there just because I don't remember why he sees an Elliot on some stairs or something walking. He looked at her with a degree of earnest admiration, which she could not be insensible of. She was looking remarkably well. Her very regular, very pretty features had been restored by the fine wind.