Here is what the Guide to the Watering and Sea-Bathing Places (1803) has to say about Dawlish:

DAWLISH.

The mild and genial softness of the air, on the south coast of Devon, is generally esteemed equally salutary for invalids with that of Montpellier, or Nice ; and, therefore, it is frequently prescribed for persons labouring under pulmonic disorders, and all the long train of complaints known under the vulgar name of declines. But, independent of health, pleasure has erected her standard, in several stations, on the southeast coast of this extensive county ; and between the entrances of the Exe and the Dare alone we find four places of public resort, Dawlish, Teignmouth, Shalden, and Torquay.

Dawlish, lying about 184 miles from London, from small fishing cove, has, within a few years, risen into a stare of comparative elegance and extent. At first it was resorted to by those who wished for more retirement than they could enjoy at well-frequented places ; but, by degrees, its pure salubrious air, the conveniences it afforded for bathing, and its natural beauties, pointed it out as an eligible summer retreat…

Dawlish is delightfully situated in a valley, on sides surrounded by high grounds, except towards the east, which opens towards the cerulean expanse; fronting which, on the strand, are some good lodging-houses. Higher up are several other buildings, well calculated for families, which command a pleasing view of various objects ; particularly of a singular Gothic structure, erected by Sir William Watson. This pile has a kind of arcade in front, with columns and pointed arches, decorated with escutcheons and fret-work pinnacles. It stands in a garden filled will various exotic plants, on one of the cliffs, and proudly looks down on the shore, which it command, for a considerable way, both towards Teignmouth and the opening of Torbay. Nearer the sea, a mount, imitating a natural rock, has been raised, with a cell in the interior.

Farther up the vale, a range of neat buildings present themselves ; among which are the two inns, which furnish tolerable accommodation. Opposite is an over-shot water mill, which has a very romantic effect ; and higher up, where the valley contracts, are several genteel lodging-houses, fronting the sea ; and each possessing a small plat before it, neatly railed in.

From hence to the church is a continuation of straggling cottages on each side the road, for the space of half a mile. Here we come to a bridge, contiguous to which is another mill and two pleasant dwelling houses. The manor-house, with its bell cupola and high poplars, increases the beauty of the picture while the church, a handsome Gothic pile, with its surrounding elm-rows, gives a kind of finish to the scene. The south part is very fine ; and between each of the ramified windows is a niche, with the remains of mutilated statues, which probably exercised the fanaticism of the round-heads, in the civil wars. The walls are adorned with battlements and pinnacles ; and near the east end is a projecting turret, in a similar style of architecture, which serves as a staircase to the roof.

The vicarage-house, encircled by gardens, is a charming spot. A high hill shelters it from the north and a screen of elms shades it on the west.

Though there is no regular market at Dawlish, it is pretty well supplied with necessaries from the neighbourhood; and besides, there is a frequent communication with the towns of this quarter, and thrice a week with the city of Exeter.

The bathing machines are numerous, and well conducted. The beach in front of the lodging-houses has a gentle descent to the sea, which is generally pure and clear.

The promenade is kept in excellent repair, and extends its a straight line across the strand. It may be lengthened at pleasure by a ramble under the cliffs, which are here bold and precipitous, and of a tremendous height; though not of a very dense and compact stratum, as is evident from the effects which the waves have produced upon them.

Teignmouth was ,as I have said larger and more cosmopolitan:

TEIGNMOUTH, in Devonshire, derives its name from its situation at the efflux of the Teign, by whose estuary it is separated from Shaldon, another Bathing Place of modern date... The Teign rises on the forest of Dartmoor, near Gidleigh. The country through which it runs is uncommonly wild and romantic, adorned with woods, rocks, and other picturesque scenery. The famous Iogan, or rocking stone, now fixed, lies in its track, and at no great distance on the left bank is a Cromlech, with other curious monuments of antiquity. Its mouth is nearly blocked up with sand, and at low water is almost impassable for vessels of any description.

Teignmouth is, distant 137 miles from London, and 12 from Exeter, is noticed in the chronicles of ancient times. Here the Danes, who were sent to reconnoitre the coasts of Britain, landed about the year 800, and having defeated the natives, spread their ravages into the interior of this country. In later times it was plundered and partly burnt by the French; but, Phoenix-like, it rose with superior beauty, from its ashes. As a memorial of this disaster, one of she streets has the name of French-street. It is divided into two parishes, East and West Teignmouth, separated from each other by a rivulet called the Tame. From the north and north-east winds it is sheltered by rising hills, near the foot of which stands the pleasant village of Shaldon in front, and the wide expanse of ocean on the east.

WEST TEIGNMOUTH formerly had, by charter, a market on Sundays, which continued to the time of Henry Ill, when this irreligious practice was forcibly put down by the sheriff's possd. There is still, however, a market every Saturday, for poultry, butcher's meat, fish of various kinds, butter, vegetables, and fruit. By an excellent local regulation, the inhabitants are allowed to supply themselves with fish, before any is sold to the dealers. Salmon, salmon-peal, sea-trout, whiting, machare!, and other kinds of choice fish, are caught here in abundance.

There are several good houses here: Teignmouth House, the residence of Mr. Baring; Bitton, the seat of Mr. Praed; and Mrs. Boscawen's cottage, have each their appropriate beauties.

The church , standing near the centre of the town, is built in the form of a cross; its roof is curiously supported by the ramifications of a wooden pillar, running up the middle. Here are several neat monuments. The whole interior is commodiously fitted up. This church is appendant on the living of Bishop's Teighnton.

EAST TEIGEMOUTH.

THIS is now the grand resort of company, as the best lodgings are situated in this quarter, which may be hired, furnished or unfurnished, at the option of the renter.

The PUBLIC Rooms is a neat brick building, containing tea, coffee, assembly, and billiard-rooms. A ball is held here every fortnight or three weeks, sometimes oftener, according to the wishes of the company.

The THEATRE, built on a spot of ground given by Lord Courtenay, is fully adequate to the purpose for which it is intended. It will, no doubt, improve with the encouragement the manager receives.

The BATHING MACHINES are sufficiently commodious and well attended. The beach, composed of velvet sands, with occasional layers of small pebbles, gradually slopes to the sea.

Later in the summer of it is thought 1802 they went to Tenby in Wales, and most probably on to Barmouth (also in Wales) too.

Here is Cary's 1812 map of England and Wales:

This is his map of South Wales showing Pembrokeshire, where Tenby is to be found. You can see it on the top left hand side of the map, just above the wording "Carmarthen Bay"::

And this is his map of the same date, showing North Wales and Merionethshire where you can see Barmouth, just below Harlech:

The Reverend John Malham in his edition of Crosby's Complete Pocket Gazetteer of England and Wales ( 1807) has this to say of Tenby:

Tenby, Pembrokeshire.

A market town situated near the mouth of the Severn-sea on the declivity of a hill about 7 miles East of Pembroke. It is a neat , agreeable well built town having a convenient harbour or road for shipping with a good quay and a considerable coasting trade to Ireland and Bristol. The church is a large handsome edifice of a very ancient appearance., with a lofty spire and 3 broad aisles and has a carved ceiling formed ( in a singular manner) of wood ornamented with various armorial bearings and supported by human figures surmounted on pillars of wood: in the interiors are several fine and well preserved old monuments.

The main street of Tenby is situated on the top of the steep declivity above-mentioned. The municipal government is conducted by a Mayor and bailiff. Here are some remains of an antient castle and in particular a spacious hall of 102 feet by 20, above and under which are noble apartments with extensive offices: these venerable ruins are now the property of Lord Milford. Of late years Tenby has become a very fashionable place for sea bathing. The season usually commences in May and closes about the latter end of October. A picturesque view of the town, but deficient of trees, is afforded from the bay.

Of Barmouth,here shown around 1805

he has this to say:

Barmouth, Merionethshire.

A small seaport town, much frequented during the season for the purpose of bathing. It is the port of the county and has a delightful walk along the beach on the banks of the river Maw.

After this sojourn around north and south Wales, the family visited Edward at Godmersham and then James at Steventon, their old home in Hampshire.

But perplexing times were about to begin......