I don't think that there is any real strongholds anywhere near here. A freind on Durham Bird Club Forum thought he saw one at Croxdale Estate not so long ago but it was unconfirmed. I don't think that there is anywhere in the County that is a really good spot for the Lesser Spotted Woodpeckers.
Potteric Carr in Doncaster has 1 pair of them :-O that's the closet place to here that I know of that has Lesser Spotted Woodpeckers.
Here is something from Gateshead Bird Club website:
http://www.gatesheadbirders.co.uk/Rarebirds/Rarebird3.htm
I hope this is of some help,
Andrew Kinghorn
ps. In 2007 there where 9 recorced in the County.