If you’re up for another 900m of ascent from Tsminda Sameba, this quite strenuous walk rewards with spectacular views. The path heads straight up the ridge behind the church; an alternative route, more protected on windy days, runs up the left flank of the ridge. The two meet at a cairn at 2960m altitude, from where a path leads on up towards the left side of the Gergeti (Ortsveri) Glacier as it snakes its way down from Mt Kazbek. Head up here for about one hour for views of the glacier, then return. You’ll need about nine hours to get up there from Kazbegi and down again the same day.
If you have a day in hand and are experienced on ice or have a good guide, it’s possible, with a further 600m of ascent, to cross the glacier and climb to the Betlemi Hut (per person US$10), formerly a meteorological station, at 3652m, where you can sleep. The hut has bunks and beds, but bring food, a warm sleeping bag and cooking gear. You can camp for free but the wind can be fierce.