There are quite a few SSiWers in the Coventry/Birmingham area - I don’t know which ones will be coming to the party or when, but it might be worth you checking out this thread to ask for lifts in case they don’t see your post here.
As for where to stay between Birmingham and Caernarfon, the train does stop at various places on the North Wales coast - you could go all the way to Bangor and stay there for the night or you might want to stop off in Conwy and see the castle.
The buses will take considerably longer but would go through some very pretty inland towns/villages, especially one that went along the A5 - Llangollen or Betws y Coed could be stops on that route.