Home base in North Wales

Using Chester as my base worked for me, and I took two day-trips into North Wales, but I'm guessing Bangor would save some back-and-forth time on trains/buses. I only passed through Bangor and don't remember it.

We selected Caernarfon for proximity to what is important to us, but we will have a car. Conwy looks charming enough but too small, too out of the way.

I agree that Conwy is very small. I was happy to spend a couple of hours (at most) there and move on. As someone tied to public transportation, I do not like to base myself in tiny towns.

Bangor is not much larger than Conwy, but it is a university town so there will likely be a variety of places to eat and things to do in the evenings. And it's well connected transportation wise to the places you want to see in North Wales. I would say it's probably a good choice for your needs and definitely not touristy.

Chester does make a good starting point for the north coast since Conwy and Beaumaris are close enough. Stay at Betws-y-Coed, go hiking or biking. Stay on Isle of Anglessy or Bangor. Go to Caernarfon and Llanberis. Go to Harlech Castle. Etc. You can do this by Train or Bus. A car is easier because it saves time from backtracking and making connections.

Personally I would stay in Chester, of Betws-y-coed. Bangor is a university town, and has some nice views out over the Menai Strait, but it's not really a touristy place. I thought it was a bit down at heal last time I was there. Not somewhere I'd personally want to base myself for a holiday. Caernarfon on the other hand is really nice, and I've had friends who've happily based themselves there for a few days. Lovely castle and again views of the Menai Strait.

In 2016 we spent five nights in Caernarfon staying at the Victoria House B&B. The location worked well for us and Victoria B&B and the host were very nice. We had a car.

We used Caernarforn a few years ago, and also stayed at Victoria House B&B. Will be doing the same thing again, on this year’s trip. We had, and will have a car, so I can’t speak to public transportation. We chose Caernarfon for the castle.

Caernarfon is also on the Welsh Highland Railway - see https://www.festrail.co.uk
Caernarfon is a nicer place than Bangor - although Bangor is served by mainline trains. Chester is OK for a quick day trip by train to Conwy (Conway) & Llandudno. However, it is too far east to be a good hub base for the most scenic parts of NW Wales but its certainly worth a visit or perhaps an overnight when entering or leaving North Wales.

https://www.traveline.cymru is the main site for finding public transport in Wales. You could try some tests to see how easy it would be to reach some of the main attractions from a base at:> Conwy / Bangor /Caernarfon and maybe Porthmadog. (As well as the Welsh Highland Railway, Porthmadog also has the Ffestiniog narrow gauge steam railway and a ‘normal’ railway that runs along the coast called the Cambrian Line - BUT - the trains are only every other hour. Places you may wish to reach = Bodnant Gardens (easiest from Conwy/Llandudno Junction; Snowdon Mountain Railway - which starts at Llanberis; Portmeirion (easiest from Porthmadog).

https://www.scenicrailbritain.com/regions/wales
https://www.visitwales.com

We also chose Caernarfon for the castle. The Welsh Highland Railway was great. I spent twenty minutes discussing their track occupancy control system with the conductor.