If you're staying near Houghton, its only 40 mins into the Durham dales. Lots of Black Grouse and breeding waders on the moors (easiest at Langdon Beck, approx 1 hr from Houghton), Wood Warblers, Pied Flys, Tree Pipits, Green Woodpeckers, Redstarts etc at Muggleswick and Hamsterley Forest. There's the excellent seabird colony at Marsden about 20 mins away (breeding Razorbills, Kittiwakes, Fulmars, large Cormorant colony). The Tees Marshes and RSPB Saltholme are only about 30 mins away - currently has Avocets, Little Egrets, Great White Egrets, Bittern, Garganey, plus passage waders.
If you want just a few more local walks, Rainton Meadows at Houghton has a good range of commoner species, plus Willow Tits, Tree Sparrows. The DBC reserve at Castle Lake, Bishop Middleham (about 20 mins from Houghton) currently has Garganey, breeding Yellow Wags, Tree Sparrows, Corn Buntings, Grey Partridges etc.
You don't have to venture far to see some top quality birds in County Durham.
Mark