Do Carlisle! Maybe I'm biased though...
Looking at around £7-8 return or an Explorer. That, or if you get a Stagecoach service (0845 or 0945 from Eldon Square) you can get a North West Explorer which gives you unlimited travel in Carlisle and beyond. Could do the "Marra Express" Stagecoach Gold 300 to Workington and back.
RE: Arriva North East: Latest News & Discussion - August 2015