score:7
Driving from Liverpool into North Wales is a pretty poor choice, as you end up paying the toll in the Mersey Tunnel, then driving most of the way to Chester to cross the Dee, so you're adding a lot of miles to your drive for no particular benefit.
Chester is a reasonable choice, but you're going to do a lot of miles on the A55 across North Wales before you get to any of the places that you're interested in getting to. Given UK fuel prices, that's adding cost without any good reason.
I would suggest Llandudno. Google Maps has eleven car rental locations in Llandudno, which should be enough competition to keep prices sensible, and there are five direct trains (taking three hours) every day from London Euston.
Llandudno Junction Station is three miles from the centre of Llandudno, but there are two car-hire places - an Avis and an Enterprise - directly outside the station. Make sure you book for the (small) town of Llandudno Junction rather than the (larger) town of Llandudno
Upvote:3
Chester looks a very reasonable choice. You can get a direct train from Euston (2 hours) and Avis looks to have an office right by the station. Definitely book the car in advance though as it's a small place and they're not going to have a big range available.
Disclaimer: I've never actually been to Chester but Liverpool is a large, unpleasant city and worth avoiding.