Itinerary ok?

We visited South Wales in 2017 renting a car from London and visiting places in England as well.

We did two nights in Cardiff, coming in from Bath, stopping at Tintern Abbey and a couple of castles (many castles in Wales and the English border). Stayed in downtown Cardiff, visiting Cardiff Castle, on the way to Tenby, we stopped at the Museum of Welsh Life that was nice.
We did two nights in Tenby, seeing more castles on the way there and then on our way to St. Davids. Not sure about four nights there, but I would recommend at least three nights. We also, visited a small sheep farming village in SW Wales were my paternal ancestors came from to America in 1716. The people are friendly and many speak the Cymru language as well as English.

We also did a shorter trip to North Wales visiting Conwy and other areas nearby some years ago when our cruise ship stopped in Liverpool.

We too had a rental car so our itinerary was somewhat different. I think you could limit St. David’s to three nights since there is little to the town itself. We spent three nights there are walked parts of the Pembrokshire coastal path on two days. The bishop’s palace was ok and the cathedral interesting as the back part leans towards the rear due to settling and because of that, parts have been rebuilt twice. We spent one night in Aberystwyth and that was more than enough. That’s the only town where the hotel wanted cash payment.

Without a car, I’m not sure how you’d do it, but for bird watching you might want to look into visiting South Stack lighthouse on Anglesey. It has a bird observation area.

If you’re an Alice in Wonderland fan, in Llandudno there are sculptures of the characters throughout town.

We skipped Portmadog and Cardiff, but did spend three nights in Tintern visiting the Abbey and nearby castles and towns. Traveling by public transportation, what you have planned seems very workable.

Not knowing exactly what you have planned for each stop, it is difficult to estimate whether you have allowed enough time for each place. 4 nights in St Davids is only effectively three days there. There is some superb walking along the Pembrokeshire Coastal path and you can also do boat trips to the islands. See here for ideas.
Along with the cathedral and ruined Bishop’s palace, you will easily ill up three days.

In Aberystwyth, try and do the trip on the Vale of Rheidol Railway . It is a delightful run to Devil’s Bridge. Depending on train times, you may have chance to do all (or part) of the waterfalls walks.

Porthmadog gives you chance to visit Portmeirion, a delightful Italianate village and there are some good walks around the estate and area. Ideas here.
There is also Beddgelert too.

I’d possible cut Caernarfon to one night and add another night to Llandudno. There is the Great Orme - as well as easy walking on the top, the bronze age copper mines are also worth visiting. Use the Victorian Tramway to get to the top. Conwy, a walled town with ruined castle and Elizabethan Town House (Plas Mawr) is worth spending time in - regular bus service between the two. I prefer the castle to that of Caernarfon asa more of the interior structures survive and you really do get a feel for what the original medieval castle would have been like. There is also the Conwy Mountain walk.

I assume you have checked out travel times between the different places and they are practical? I also assume you are catching a train back to Cardiff from Llandudno rather than trying to get there by bus?

Two nights is only one day somewhere, so your trip is rushed. I would drop Swansea.

I have spent three weeks in St David’s, walking various sections of the coastal path and bird watching.

I am not a fan of Aberystwyth. RSPB Ynys-Hir between Aberystwyth and Porthmadog is excellent for bird watching, but isn’t easy to get to by public transport.

I would opt for either Caernarfon or Llandudno - the latter would be my choice. Conwy nature reserve is a good spot for birding, near Llandudno Junction train station.

You don’t say which airport you are arriving at. You could consider Manchester if flights available from wherever your start point is in USA.
CARDIFF - be sure to visit St.Fagans Castle & Museum - about 7 miles W of city centre - Cardiff Bus from Westgate Street (stadium side). Also suggest local train to Caerphilly to see wonderful medieval castle (but town is a dump). On returning to Cardiff, you may like to get off at first stop after tunnel (Lisvane) - walk over footbridge & across car park - L & then R into Cefn-Onn-Park. Return to train and go to Cardiff Bay (change at Queen Street). To do all that, probably best to buy a Cardiff Valleys Day Ranger ticket - see >
http://www.railrover.org/index.html Castell Coch on northern edge of city is another possibility - bus to Tongwynlais and then 20 minute walk up hill and of course, Cardiff Castle and the National Museum of Wales in the city centre.

Best to take train to SWANSEA but as has been said, if you want to skip anywhere, I would make it Swansea. If you do go to Swansea, Rhosilli on the western tip of the Gower peninsula is the place to take a day trip using the local Adventure Bus. Lovely Bays SOUTH of the car park - follow track around fields. If just staying in Swansea, take a local bus to Mumbles. Best to use the train between Cardiff & Swansea. Also best to use the train between Swansea and Tenby - best views are on the left.

TENBY - go to harbour and local boatmen run a shuttle service over to Caldy Island - not Sundays.

Bus to ST.DAVID'S (change at Haverfordwest). I think that 4 nights in St.David’s is too long.

You will need buses to get from St.David’s to Aberyswyth. If possible - break journey at Aberaeron to see beautiful harbour with coloured cottages. ABERYSTWYTH - be sure to travel on Vale of Rheildol Railway (steam).

Although you can go by bus from Aberystwyth to Porthmadog, the railway follows an even more scenic route - change required at Machynllleth or Dovey Junction. The train calls at the lovely estuary village of Aberdovey. You may like to consider getting off at Barmouth and continuing on a latter train. Harlech is another stop further up the Cambrian Coast Line and you will see a castle high above the railway. On http://www.railrover.org/index.html the Cambrian Coast Day Ranger might be cheaper than buying tickets.

PORTHMADOG - be sure to visit Portmeirion. Also take a trip on the Welsh Highland Railway to Caernarfon. If staying in Caernarfon you may like to consider going by bus to Llanberis to take the mountain railway up Snowdon - or hike it. If you want to go from Porthmadog to Llandudno, consider taking the scenic Ffestiniog narrow guage steam railway to Blaenau Ffestiniog (an old slate mining town) and then the ‘normal’ train to LLANDUDNO - where you perhaps should add a night or 2. (From Llandudno - suggest you take a local bus to Bodnant Gardens. You will should also go to Conwy to see the Castle).

To get from Llandudno to Cardiff - take the train. However, I would also suggest that you either stop off or take 1 night in CHESTER - which also has direct trains to Manchester Airport - as does Llandudno. If going by train back down to Cardiff - as well as Chester, Shrewsbury and Ludlow are on this route and worth a look. However, you can take fast direct trains back to London (Euston) from north Wales/Chester. (It may be cheaper to buy a ticket to Crewe and then an advance specific train ticket from Crewe to EUS).

https://www.traveline.info
Trains:>https://www.traintickets.com/?
https://www.railcard.co.uk
Longer distance train journeys are cheaper if booked in advance for specific trains. For short hops - pay on the day.

Longer distance buses in Wales (but some are more like local buses) =https://traws.cymru/en

As James has highlighted, you are trying to fit a 6 week trip into half that! Your choice of what you want to see and what you need to drop.

I would drop Swansea, Porthmadog and Caernarfon to avoid it being rushed.

I had a look at Yns Hir. There is a restaurant there where meals start from £350.00 !
You can have a week abroad for less than that. Think i will give it a miss

roger - the Yyns Hir to which you refer is a restaurant with rooms where people pay ridiculous prices for food. This area on the south side of the Dovey (Dyfi) estuary is called Ynys Hir and the RSPB (Royal Society for the Protection of Birds) have a base nearby - nothing to do with the restaurant/hotel.
https://www.rspb.org.uk/reserves-and-events/reserves-a-z/ynys-hir/

3 years ago, I drove off the main road to the Dyfi Osprey Project - which is near to Dovey (Dyfi) Junction train station = a lonely place in the middle of a vast bog.
https://www.dyfiospreyproject.com.

Here is a Google Map of the area.

A big thank you to everyone for your fantastic suggestions. They are immensely helpful and encouraging. Trip planning can be overwhelming! Thanks again and happy travels