Each and every monument has an interesting story to tell. Stop at Obelisk of Thutmoses I and learn a little about the area's history.
You're spoiled for sightseeing choice when staying in Luxor. Obelisk of Thutmoses I is a great place to start here, but there are numerous other worthwhile places to visit. Valley of the Kings, Luxor Temple, and Karnak are near the commemorative structure and and will cap off your day nicely.