WHERE TO GET MAPS
If you are looking for paper trekking maps, the best place to get some is Geoland store in Tbilisi. It offers maps of most of hiking destinations (sadly, Samegrelo is still missing). Shop is open from 10 am till 6 pm, closed on weekends.
In Svaneti, you can get solid hiking maps for free in Mestia’s InfoCentre at the main square. Another good place is the souvenir shop at the Seti Square (behind the Koshki café), it sells hiking maps from several publishers (Geoland, Terraquest and so on).
There is also a small enterprise named Hiking maps of Tusheti which, as the name suggests, sells hiking maps of Tusheti. Maps can be bought at Tusheti tower guesthouse in Upper Omalo as well as in Kvemo Alvani village at the shop at the crossroads, from which depart jeeps towards Tusheti.
Probably the best hiking maps of Georgia available online were made by Geoland, based on Russian military maps. They can be found at the address http://mygeorgia.ge/geotrails. By default, they show hiking trails in Khevsureti, but with some scrolling can be used for any other region in Georgia. If the link doesn't work, solid hiking map of Georgia is ofered for example by http://mapy.cz.
If you are for some reason interested in original Soviet military maps, those are accesible too. However, for a Westerner they can be quite cryptic as they use Cyrillic script. Maps can be accessed here.
Russian mountain enthusiast Mikhail Golubev took these slices and created from them huge map of whole Southern Caucasus. It can be downloaded here.
If you want to use smartphone for navigation, I recommend to install Locus maps. Then you can download very good topographic map of Georgia, which can be found at http://www.openandromaps.org/en/downloads/asia-middle-east.
There is also an Android application containing all military maps mentioned above, it's name is "Soviet Military Maps". It can be installed for free from Google Play.