The sulphur baths of Abanotubani are the reason Tbilisi exists — legend says King Vakhtang Gorgasali discovered the hot springs while hunting in the 5th century and founded the city on the spot. The domed brick bathhouses clustered at the foot of Narikala Fortress still draw from those same sulphurous springs.
You have two options: a private room or the public baths. Private rooms at places like the Orbeliani Baths (the blue-tiled facade you see in every photo) or the Royal Bath run around 50-80 GEL per hour and come with a large tiled pool, steam, and the option of a scrub-down from a mekise (bath attendant). The public bath at Bath No. 5 costs just a few lari and gives you the more authentic, no-frills experience.
The sulphur smell is strong but you stop noticing after a few minutes. Your skin will feel remarkably smooth afterwards. Go in the evening when locals come after work.