Final answer:
Chichen Itza is the archaeological site with a ball court that has the Nunnery Complex in the background, featuring the largest and best preserved Mesoamerican ball game court.
Step-by-step explanation:
The archaeological site that features a ball court with the Nunnery Complex in the background is Chichen Itza. Chichen Itza's Great Ball Court is the largest and best preserved court for playing the Mesoamerican ball game, which was an important sport with ritual associations that has been played since 1400 BCE. The ball court at Chichen Itza is noteworthy not only for its size but also for the presence of detailed carvings depicting the ball game, including imagery of players and ritual sacrifice.