Summer is almost upon us though perhaps you wouldn't know it by the rainy weather at present! Regency seaside resorts became very popular in the late 1700's/ early 1800's. Jane Austen loved Lyme Regis and even used the town in her book Persuasion. Here are a couple of extracts from a letter she sent to her sister Cassandra on Friday, September 14th 1804. ...I continue quite well; in proof of which I have bathed again this morning. It was absolutely necessary that I should have the little fever and indisposition which I had: it has been all the fashion this week in Lyme...The ball last night was pleasant, but not full for Thursday. My father staid contentedly till half-past nine (we went a little after eight), and then walked home with James and a lanthorn, though I believe the lanthorn was not lit, as the moon was up, but sometimes this lanthorn may be a great convenience to him. My mother and I staid about an hour later. Nobody asked me the two first dances; the next two I danced with Mr. Crawford, and had I chosen to stay longer might have danced with Mr. Granville, Mrs. Granville's son, whom my dear friend Miss A. offered to introduce to me, or with a new odd-looking man who had been eyeing me for some time, and at last, without any introduction, asked me if I meant to dance again. I think he must be Irish by his ease, and because I imagine him to belong to the honbl. B.'s, who are the son, and son's wife of an Irish viscount, bold queer-looking people, just fit to be quality at Lyme. 
I think the following description from Persuasion sums up Jane's own feelings about the place. She rarely used description of this sort to such an extent. Anne Elliot travels to Lyme with her sister Mary and husband Charles, his sisters, Henrietta and Louisa, and the hero of the book Captain Wentworth.After securing accommodations, and ordering a dinner at one of the inns, the next thing to be done was unquestionably to walk directly down to the sea. They were come too late in the year for any amusement or variety which Lyme as a public place, might offer. The rooms were shut up, the lodgers almost all gone, scarcely any family but of the residents left; and as there is nothing to admire in the buildings themselves, the remarkable situation of the town, the principal street almost hurrying into the water, the walk to the Cobb, skirting round the pleasant little bay, which in the season is animated with bathing-machines and company; the Cobb itself, its old wonders and new improvements, with the very beautiful line of cliffs stretching out to the east of the town, are what the stranger's eye will seek; and a very strange stranger it must be, who does not see charms in the immediate environs of Lyme, to make him wish to know it better. The scenes in its neighbourhood, Charmouth, with its high grounds and extensive sweeps of country, and still more its sweet, retired bay, backed by dark cliffs, where fragments of low rock among the sands make it the happiest spot for watching the flow of the tide, for sitting in unwearied contemplation; the woody varieties of the cheerful village of Up Lyme; and, above all, Pinny, with its green chasms between romantic rocks, where the scattered forest-trees and orchards of luxuriant growth declare that many a generation must have passed away since the first partial falling of the cliff prepared the ground for such a state, where a scene so wonderful and so lovely is exhibited, as may more than equal any of the resembling scenes of the far-famed Isle of Wight: these places must be visited, and visited again to make the worth of Lyme understood.
If you go to Lyme you will be pleased to see that it has not changed much since Jane Austen's day. Many of the buildings have survived from that time and the little town has a Regency air.