Makhuntseti is the classic quick mountain excursion from Batumi: a stone arch bridge from the old Adjara road network and a waterfall set in a green valley. The bridge is small but elegant, and the waterfall gives the trip the cool, damp air missing from the summer seafront.
It is easy to over-romanticise as untouched countryside, because the site is popular and accessible. Go early if you want it quiet, and treat it as an introduction to inland Adjara rather than the deepest mountain experience in Georgia.