Teesdale itself doesnt get a lot of tourists, between barnard castle and Alston there is only one indoor visitor attraction – Bowlees visitor centre.
On bikes – Hamsterly Forest or about 30mins to Reeth and Dales Bike Centre in Swaledale.
Off bikes – Barnard Castle Castle, Walks along the Tees – head west to Eggleston Abbey (not near eggleston village). Bowes Museum – worth looking at from the outside, French Chateau. Inside depends on how much you like your art. Not sure if they still have the mutant two headed calf in a case these days.
Upper Teesdale – waterfall walks from Bowlees. Park at visitor centre then go to Low Force and on up to High Force. Also check Gibsons Cave. Longer walk – start in Middleton and follow Pennine Way to High force and back. Tourist Information in Middleton in Teesdale – good cafes. Cow green and walk down to Cauldron Snout.
Car tour – Start in Barnard Castle then B6277 to Middleton, B6277 to Alston. A689 to Stanhope, B6278 back to Middleton. Enroute – Bowlees and Low Force, High Force, Alston – galleries, steam trains and stuff, Nenthead – mining stuff, Killhope – mining museum and big waterwheel, Ireshopeburn – small museum, Stanhope – steam trains.
Mountain biking – mostly moorland. Hamsterly – Eggleston – Hamsterly good if dry. I think best done anti clockwise. Bowes moor is more of a dry summer riding thing.