update tourism_catlinks 
join tourism_links on tourism_links.id = tourism_catlinks.LinkID_tourism_catlinks
join tourism_category on tourism_links.geo_town = tourism_links.geo_town and tourism_links.geo_county = tourism_links.id
set tourism_links.LinkID = tourism_links.id

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Your SQL ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

update tourism_catlinks 
join tourism_links on tourism_links.id = tourism_catlinks.LinkID
join tourism_category on tourism_links.geo_town = tourism_links.geo_town and tourism_links.geo_county = tourism_links.id
set tourism_catlinks.LinkID = tourism_links.id


^ Edited SQL, had to drop the second part of tourism_catlinks.LinkID_tourism_catlinks due to 'unknown column'