We are visited England and Scotland and would like to visit Wales and spend about 3 or 4 days, especially in or around Conwy. We will be traveling only by train or bus. Any suggestion other than visiting Conwy.
The main operator of trains in Wales is Arriva...there are other lines available. And special excursion lines. So it looks feasible to take the train with short connecting bus rides. You may be able to book a tour to some of the sites from train stations. Be sure to get a CADW pass if you want to see most of the castles.
This place is near Conwy but may not be worth a visit in winter:>http://www.bodnantgarden.co.uk
Also go to the nearby seaside town of Llandudno.
From Llandudno Junction = 1 mile E of Conwy, you could take a train up the Conwy/Conway Valley to Blaenau Ffestiniog and then ride the narrow gauge Ffestiniog Railway demo the Porthmadog. From Porthmadog, another steam railway - The Welsh Highland - will take you to Caernarfon (Castle). From here, you could take a bus back to Bangor & then a train to Conwy. You will need to check the schedules as it is quire a long day out and might work better in the reverse direction.
Trains - www.nationalrail.co.uk
Buses:> www.traveline.info though in Wales, this site might be better - http://www.traveline.cymru