Some of the spots you would want to reach by the end of the day include Drass, Kargil, Mulbek, Lamayuru, Alchi and Likir. These spots have quite a few hotels where you can freshen up. Other than that, most monasteries could be emergency shelters for tourists.
Check out the Manali to Leh bike tour which gives you a chance to explore the beauty of Manali and Leh.