UVA libraries do not offer individual-level-subscription access to periodicals. Our access to periodicals comes as part of database subscription packages.
Journal Finder is our site where you can type in the title of any periodical you're interested in (newspaper, academic journal, popular magazine) and get all online access portals including information on which time periods they cover: https://guides.lib.virginia.edu/journalfinder
Many of these databases offer PDF downloads, but access varies.
Worth noting: if you are a UVA student, you can often use your student status to get a discounted subscription or extended free trial to many newspapers/magazines/periodicals.