In Batumi I happened to know where there was a ticket office in the old town to buy railway tickets because I lived nearby. But it had no sign at all and would be very difficult to find if you didn't already know it was there. It was very handy though because the train station was 5km outside the city.
But now I'm in Tbilisi and the long distance train station is also not very handy but I don't know, and can't find on the internet, if there are also Georgian Railways ticket offices here besides at the station.
I've looked at Wikitravel and the Georgian Railways website and don't know where else to look.