By Car/Marshrutka
The principal route to Akhaltsikhe runs from Georgia's main East-West highway E60 at the spur in Khashuri leading to Borjomi. Marshrutkas run to Akhaltsikhe's main market/bus station from Tbilisi's Didube market, as well as from the bus stations in Kutaisi and Khashuri. Coming from Kutaisi or Tbilisi, it's best to catch your ride early in the morning if you want to avoid finding another marshrutka upon arrival in Khashuri. But it's not terribly difficult to catch a marshrutka going between Akhaltsikhe and Khashuri before dinner time.
By train
Akhaltsikhe is connected to the main Batumi–Tbilisi–Baku railroad by a spur through Borjomi ending in Akhaltsikhe itself. You should be able to find a train going this way once daily from the Batumi, Kutaisi, and Tbilisi train stations.