Cholokashvili Street is Telavi's most pleasant old-town walk, with renovated facades, balconies, and a quieter feel than the traffic around the main square. It is not a museum-piece street, and some of the restoration is smoother than the old town probably was, but it gives you a useful sense of the historic centre.
Use it as a slow connector rather than a standalone sight. Wander it after Batonis Castle, then loop back toward the market or the wine shops near the centre.