宿 lodge at

it sounds AND looks like 新宿, so that's easy to remember.

At the crown hotel is so big, a hundred people can lodge there.

Shinjuku ward ★★★☆☆
新 (new) + 宿 (lodge at) + 区 (ward) = 新宿区 (Shinjuku ward)

homework ★★★☆☆
宿 (lodge at) + 題 (topic) = 宿題 (homework)

stay the night ☆☆☆☆☆ NP
宿 (lodge at) + 泊 (stay for the night) = 宿泊 (stay the night)

the act of staying the night -(kind of formal; you might read it in a hotel guidebook, but you wouldn't say "Let's 宿泊 over there, guys!"