Nokalakevi is an ancient Colchian fortress built on the banks of the Tekhuri River. It's been mooted as one of the (many) places to have housed the Golden Fleece, and is well worth a detour to explore, not least for the impressively engineered tunnel on the far side of the complex leading down to the river. Admission includes an interesting archaeological museum, a new building for which was under construction at research time. Excavations are ongoing (see www.nokalakevi.org).
About 1km upstream along the Tekhura you can take a dip in soothing thermal pools.