Close by there is skilled scrambling on the famous Pudding Stone - on this large boulder alone there are 30 different challenging routes. Not much further away there are classic climbing and scrambling routes on Dow Crag, probably the best crag in the Lakes, with classic routes for every grade, and with views down towards the Pennines.
See the UK Climbing Pudding Stone or Dow Crag web pages for details.
Not too far away, in Langdale, there is the famous Jacks Rake scramble, which is good for the intermediate to advanced scrambler, while Middle Fell Buttress is a stunning all weather climb offering exposure and great views. The Bowfell Buttress is a famous climb in a more remote location.
For all local climbs, see UK Climbing (20 miles radius) web page.