Seaside Wales without a Car

Given the limited time you have I'm not sure that travelling to North Wales is the most productive way to do it, especially given the ongoing uncertainty over rail strikes.
I think I would rather stay in South Wales, where you will be covered with a mix of local bus and National Express Coaches back to Cardiff and Bath if strikes happen.
It is worth considering Swansea and the Gower Peninsula. Swansea is only an hour from Cardiff.
But also Tenby and St David's are a great idea. Both have access to the Pembrokeshire Coastal path, wonderful beaches and little off shore islands.
With the cancellation this summer of the three Pembrokeshire coastal buses this year, and that you are fairly late to booking, I think that Tenby is the better fit of the two as opposed to St David's which is an easy day trip from Tenby, as Tenby has much more accommodation. Change trains at Swansea for Tenby.
https://tfw.wales/

This is the Pembrokeshire bus timetables web page-
https://www.pembrokeshire.gov.uk/bus-routes-and-timetables/bus-routes-list-all-buses

If staying at Tenby think about a boat trip to Caldey Island-https://caldeyislandwales.com/how-to-get-here

This website should help you with places to stay-
https://www.visitpembrokeshire.com/explore-pembrokeshire/towns-and-villages/tenby-and-penally

What time does your flight to NYC depart from Heathrow? Your airline will probably suggest you be at the airport 3 hours before departure time; if there are significant issues at the airport, earlier would be better. There are no trains direct from Bath to Heathrow; you'll have at least one transfer and may need to go into London and head back out again. This sounds risky to me, but I'm very conservative about my travel plans on departure day since I'm don't want to have to buy a very expensive, last-minute replacement ticket home.

And this website is all about visiting the Gower sustainably (without a car)-
https://swanseabaywithoutacar.co.uk/gower/

(follow the link on there for traveline cymru and thus bus timetables)

My suggestion to get to Cardiff and back from Bath to Heathrow, would be to use National Express Coaches, as they are direct journeys and not at the whim of rail strikes.
Heathrow to Cardiff is hourly (and as fast after allowing for the dog leg into London) and from Bath there is a direct coach as early as 5am, arriving Heathrow at 7am, then broadly every 2 hours through the day. Looking just now it is exciting to see the return of the £1 coach fare on the 5am service (not the typical fare, but still interesting).

I would highly recommend St David’s if you like old things and beautiful coastline. I have no idea how to get there on public transport but once you are there you’ll be able to explore quite a bit on foot. And bonus, there’s a new Premier Inn there now!

With on 3-4 days to work with I’d skip Llandudno and Conwy in the north and stick with St. David’s and Tenby in the south. Tenby offers great views of the water and a nice beach to walk on, while you can walk a couple sections of the Pembrokshire Coastal path from St. David’s. I’m sure there are other towns, but those are the ones I’ve been to. I will add that I had a rental car, so no idea about trains.

So, to clarify a bit, from the link I gave above-
To reach St David's you either go to Haverfordwest (on a train to Milford Haven) or to Fishguard & Goodwick (a new stop just before the ferry port for Rosslare in Ireland).
From either station you catch the T11 bus which takes 51 minutes to St David's from either.
The trains are-
Cardiff 0807 1007 1147 1346
Haverfordwest 1041 1238 1420 1624
The 0807 only is change at Swansea.
Buses depart from the station at 0900, 1000, 1200, 1310, 1400, 1615 and 1715 -thus the 1007 train is the one you want, advance fares are £14 on the 1007 train and later.
Return trains to Cardiff are-
HWest 0916 1118 1315 1522 1725
Cardiff 1150 1354 1545 1805 2016

Cardiff 0942
Fishguard and Goodwick 1222
The return trains to Cardiff from Fishguard are at 0957 (a 1248, change at Carmarthen) and 1253 (a 1527). The advance fare is £20.10.
Buses from just outside the station to St David's are at 0700, 0745, 1000, 1100, 1200, 1400 and 1700

For Tenby, take a train from Cardiff to Carmarthen, and change there for Pembroke Dock- Tenby is the 5th of 10 stations on this line-
Trains are-
Cardiff 0631 0745 1049 1256 1445 1704
Tenby 0932 1141 1341 1537 1738 1953
the 1704 (only) is a through train.
Advance fares are between £14 and £18 depending on train.
To reach St Davids from Tenby- take the (hourly) bus 381 at 0845, arrives Haverfordwest at 0952 then the T11 as above, return from St David's at 1507 Schooldays, 1542 Non Schooldays and Saturdays, changing into the 381 at 1700 or 1800 from Haverfordwest.
This is the only connection which works.
Coming back from Tenby trains are at 0729, 0940, 1142, 1342, 1538 and 1740, taking 2 1/2 hours and change at Swansea in this direction.

I wasn't going to post this level of detail, but 2 posters have said they don't know how to do it by train, so there you are.

From Tenby there are a variety of other bus routes on the precedent link by which to explore the area.

Pembroke Dock is another ferry port for Rosslare, Ireland. The town is worth exploring- but use the preceding station (Pembroke) not the Dock station- which is the last on the line.

All the trains I have shown from Tenby, Haverfordwest and Fishguard have connections at Cardiff for Bath.

Fares- from Haverfordwest and Fishguard- buy an advance ticket to Cardiff then another one Cardiff to Bath.
from Tenby buy a fare from Tenby to Carmarthen (where the train has to stop to reverse direction), another advance fare from Carmarthen to Cardiff, then a 3rd one from Cardiff to Bath.
That is how to split to save lots of money- I've just fiddled around to find the best way to split.

Thanks for your comments, everyone. And thank you, isn31c, for suggesting the Gower peninsula, which I had not considered before. The web site that you shared about a car free visit there is perfect.

I am now planning a couple nights in Rhossili or Mumbles, as well as a night or two in Swansea, perhaps with a day bus trip to Tenby. I also purchased a one pound early coach ticket to Heathrow from Bath for my return flight--thanks for that tip too!

Mumbles is really a part of Swansea. Clyne Gardens is a lovely wooded park just off the road between Swansea centre and Mumbles.
By public transport, you probably find it easier to reach Tenby by train from both Cardiff (it is just over 3 hours) and Swansea. Tenby is gorgeous.https://www.visitpembrokeshire.com/articles/48-hours-in-tenby

If you go to Rhossilli, you will see a beautiful beach to the north of the village. Most people then walk out towards Worm’s Head. You can walk back along the south coast where you will see Falls Bay. A path (not clearly marked) winds back around fields to the village.
Fall Bay is the first picture on this website (given to you earlier by isn) :> https://swanseabaywithoutacar.co.uk/gower/

When in Cardiff, if you take a local train to see Caerphilly Castle (about 8 miles N of Cardiff centre), on return trip you might like to get off at first stop after tunnel (Lisvane) - walk over footbridge and cross car park - then L & R into Cefn-Onn -Park.

https://cadw.gov.wales/visit/places-to-visit/castell-coch is on a hillside on the northern edge of Cardiff. Use bus.

More car-free south Wales

https://www.theguardian.com/travel/2021/aug/04/i-could-be-by-the-med-car-free-short-break-swansea-dylan-thomas-gower

Thank you, James and ramblin' on!

Thank you for posting this question. I am hoping to take a car-less trip to Wales in 2024. I'm in the beginning stages of planning (a.k.a. dreaming)

Hi, Motorgirl, I hope you have a wonderful future trip to Wales. For me, planning and dreaming is almost as much fun as doing!