https://www.tripadvisor.com/Attraction_Review-g12585339-d2487389-Reviews-Gremi_Citadel_and_Church_of_the_Archangels-Gremi_Kakheti_Region.html

https://www.openstreetmap.org/node/5981115568

Visitation details are sparse, but you can tell from comments that people do visit.

City of Gremi, capital of vanished Kachetian Kingdom of Georgia, located on the Gilian-Shemakha branch of the Great Silk Road, was destroyed by the army of Shah Abbas in XVI c. and never been restored since then. The ruins of Gremi city are now important Late Medieval archaeological site with ruins of churches, trading arcades, baths and dwellings. Gremi attracts visitors with the well-preserved architectural complex: Church of Archangels Michael and Gabriel and the Royal Tower.

The Gremi Church was built and painted upon the order of King Leon in 1565. Peculiar relation of proportions to separate volumes of Gremi Church attaches new features to traditional structure of Georgian cross-cupola churches. The main cross of the building is very high and narrow. The arches are arrowed and have not capitals or tractions. The dome is supported on two free-standing piers and the extensions of the apse. The fabric is of so-called Georgian brick. The façades are samples of developed brick church decorative system characteristic to late feudal epoch in Georgia. The forms of décor are achieved through deepening of planes and turquoise fittings. The wall painting of construction period is preserved inside the Church. The Gremi Church has become a prototype for a whole group of other church buildings in Georgia.

A three-store tower is erected beside the Church of Archangels. The two bottom floors are built earlier than the Church itself. There is a big, wide and high room on the ground floor. Along the back wall of the room, there is a corridor, which leads to the first and second floors. There is a belfry on the top of the tower.

The aspiration and rush for height of the Kachetian architecture is shown in Gremi with force incomparable hitherto. Elegance of silhouette of a Church and a Tower is an attractive architectural dominant in vast space. Through its location and interrelation with the surrounding landscape, the Gremi Church acquires outstanding artistic importance and remarkable force.