The Library of Virginia has created the Virginia Memory Project. They have saved the archived versions of web sites, many of which are related to Virginia political history. You can find the web archives of governors and the websites for statewide elections. The Library of Virginia has been collecting relevant websites since 2005.
The Library of Virginia Memory Project offers more archival web material beyond governor's administration websites. You can find more web archiving (inlcuding emails of Governor Kaine's administration) and historic Virginia government collections.