Georgian Public Broadcasting owns two of the most popular TV channels in Georgia, First Channel and Second Channel. They're website provides access to videos from some of they're most popular programs including news programs. The media network also includes access to news articles, streaming music, and radio programs on their site.
A good source for newspaper websites from all over the world is World-newspapers.com. They have country newspaper listings by region and continent, and Georgia is listed under the Europe section. Many of the sites have English and Georgian language options.