Castleton and Mam tor.

Sundays you can get a direct bus (373) to Castleton from Picadilly, otherwise take a train to Glossop and a bus from here. Castleton is a sweet little, quite toursity village in the Peak District. It has a castle ruin (hence the name) and many caves around. But even more exciting is the huge landslide at Mam tor and the valley of Winnats Pass (on the picture). Pick up a map in the national park information centre and make a days walk around the place.

Dervent and Ladybower reservoire. Take the 373 Sundays bus from Picadilly to the Ladybower reservoire. If you don't have a Peak District map yet, you can pick one up from the small visitor center. I recommend you climb up to the ridges East of the reservoires and walk North - till you feel its time to come back down. Another good idea is to rent a bike at Ladybower and cycle around the reservoires. Don't forget to visit the exibition on the Dervent dam, where you can find out what other puropses reservoires can serve besides storing water and possiby producing energy...

If you leave the paved roads to climb the hills, you need to have a map+compass and proper shoes and clothing.

York. From Picadilly take a train to York, if you have the time and money, it is worthwhile to stay overnight in this beautiful town. Once at York definitely visit the York Minster, take a boat ride on the river and go to the train museum. It is also nice to pick up some local cheese at the market, sit in the park, sip a coffee on the pedestrian streets and explore the town walls.