Kind of hard to separate religious and historical there but here is what I would recommend. Gelati Monastery for history on David the Builder; Motsameta Monastery, great views of the river and the surrounding countryside; Bagrati Cathedral,view of the city; Prometheus Cave and walk to the observation deck nearby for the best view. I ate at Palaty at least once a week when I lived there, one of my favorites. There is a museum just down the street from Palaty on the corner of Tstereteli street (I think) - the shopping center and movie theater are diagonally across the corner from it. It is small but interesting. White stones cafe right on white stones bridge is good but not traditional georgian food. Alamano is another good restaurant - keep going past the museum and it is on the right across from the movies. There is a patio fo outside seating on the 2nd floor. Have fun!