Here are a 3 walks you might want to do. I am assuming you have the OS map 315 for Carlisle, all the place names are listed on the map. All of the walks have a little bit of road walking but follow footpaths and bridleways for the most part. Enjoy your time and I hope you enjoy the walks. Geltsdale and Castle Carrock are really lovely places to go to if you haven't been already.
Walk 1
Low Gelt Bridge (car park here), Tootop Woods - Greenwell - Castle Carrock - Jockey Shield - Geltsdale - Talkin - Middle Gelt - Gelt Woods - Low Gelt Bridge Approx 9.5 miles 200m ascent
Trip report here but we walked from the bus stop at Hayton Lane End
http://www.walkingforum.co.uk/index.php?topic=36150.0Walk 2
Brampton (car park here) - Old Church Lane - Crooked Holme - Castlesteads - Walton - Abbey Gills Wood bridleway to Lanercost - Quarry Beck - Brampton Ridge - Brampton. 9 miles with 350m ascent
Walk 3
Brampton (car park here) - Dismantled railway (Dandy Dimont railway near Staith) - Brampton Station - Tarn Wood - around Talkin Tarn - Tarn Wood - Tarn Road - Wreay - Capon Hill - Brampton. Approx 8 miles