Akhalkalaki sits on a high plateau a long way from anywhere. Marshrutka minibuses from Tbilisi take around four hours and leave from the Ortachala bus terminal; the route climbs steeply once you turn off the Borjomi road. Connections from Akhaltsikhe are quicker and more frequent, about an hour and a half on a slow but scenic road.
The border crossing into Armenia is at Ninotsminda–Bavra, about thirty kilometres south. Shared taxis and minibuses run from Akhalkalaki to Gyumri, Armenia's second city — expect a couple of hours and minimal hassle at the post. A direct private taxi to Gyumri is in the region of $20 to $30.
The Kars–Tbilisi–Baku railway passes through Akhalkalaki, but at the time of writing passenger service is irregular and mainly geared to freight. Check current schedules in Tbilisi before planning a train arrival.