Think about a base around Llandudno/Conwy. It is an easy train journey from Liverpool and you could even break journey and spend a night in Chester on the way.
Llandudno is a Victorian seaside town with pier and traditional Punch and Judy show. There is the Victorian Tramway to the top of the Great Orme which also has a Bronze Age Copper mine.
Conwy is just a short bus ride away and is a medieval walled town with a ruined castle. You can walk along part of the walls. It also has a restored and furnished Elizabethan Town house too. Walk across the suspension bridge (long closed to traffic) for views of the river and castle. You can also do a boat trip too. Bodnant Gardens are a short bus ride away and there should be plenty of autumn colour. There is also Betws y Coed a bit further on the bus, or train. You can also catch a bus to Caernarfon, another walled town with ruined castle, or across to Beaumaris on Anglesay with its moated ruined castle and the Old Goal.
Catch the train or bus to Blaenau Ffestiniog, the slate capital of North Wales. The train journey is dramatic through lovely scenery and you go through a long tunnel and burst out into the completely different slate landscape of Blaenau Ffestiniog with the remains of quarry workings, waste tips and and steep inclines which brought the slate down from the hills to the town to be taken to ships at Portmadog and exported round the world. Llechwedd is worth a visit and consider doing the trip down the deep mine to find out what it was like for the Victortian slate miners. (Or if you are into high adrenaline activities, there is a zip wire too!!)
If you wanted another base in North Wales, think about Criccieth or Porthmadog. (Either train/bus to Blaenau Ffestiniog and bus or Ffestiniog Steam Railway if timetable allows to Porthmadog. Criccieth is a short bus ride away. OR catch the bus to Caernarfon and then bus or Welsh Highland Heritage Railway to Porthmadog.)
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