The Sherpa Bus network is a good alternative to the Ffestiniog Railway to get between Betws-Y-Coed and Porthmadog - and MUCH CHEAPER especially as the narrow gauge railways don’t offer one way tickets. https://www.sherparwyddfa.wales
(The Ffestiniog Round Robin ticket - which includes the normal trains, would have been OK for you if it did not have the restriction of having to do the whole journey in one day).
Anglesey inland is just flat boring farmland. The coast is nice enough but a car is really needed to get about.
I suggested staying in Porthmadog because it has transport links by rail & bus and puts you ideally located to see Portmeirion - the Italian style village. It also places you in a location where you can take the scenic Cambrian line south along the coast to Aberdovey before turning inland and heading for Shrewsbury (worth a wander when changing train routes). Tip - if using this route, ask the guard if you can just nip onto the platform at Harlech to take a photo of the Castle on a cliff high above the line. (The windows don’t open and are tinted).
It’s about a 4 hour journey between York & Conwy. I suggest you buy an Advance (specific train non refundable) ticket between York & Chester and then have a wander around the historic city centre. Then, head back to the station and buy on the day a one-way ticket to Conwy for about £13 - having first noted when the trains depart.
It’s just over 6 hours from Porthmadog to Bristol with the first scenic bit being especially slow going. You may like to buy a ticket from Porthmadog to Shrewsbury and have a look around before continuing south.
On some routes, it pays to split the ticket. It also can work out cheaper to book in advance specific trains - especially for one way journeys. This site will tell you if splits work out cheaper thought they do take 10% commission on the amount saved:>
https://www.traintickets.com/?/ (Play around with dates to compare the cost of pay on the day v advance purchase. Note that fares rise on 1st January).
It sounds like you will be travelling quite a lot by train. In that case, you should consider getting a Railcard. See >
https://www.nationalrail.co.uk/tickets-railcards-and-offers/railcards/
Also note that when you get to Newport, you will need a train going to Bristol Temple Meads (the downtown station) and not Bristol Parkway on the edge of the city.