What's your favourite wee holiday/daytrip from Liverpool that's accessible by public transport?

Hello! Over the past year we've been to Anglesey and Llandudno and would like to go on more daytrips or even short breaks from here, but not being able to drive makes it a bit trickier. (Looked at Portmeirion - four hours each way without a car. No.) Somewhere with nice scenery, good walks, good pubs, places to eat, and not so expensive that I'll remember how cheap it is to stay in other countries once you pay for the flight. Where would you recommend?