Mexico City
Most hotels near Constitution Square sit in Mexico City itself, and staying here puts the square within a few minutes on foot. The Gran Hotel Ciudad de Mexico Zocalo View is 160 m away, about 2 minutes, Best Western Majestic 130 m, also about 2 minutes, and NH Collection México City Centro Histórico 260 m, around 4 minutes. Guests here are surrounded by the historic centre's restaurants and sights. From June to September expect rain most afternoons, usually a two-hour burst, with mornings generally fine.
Cuauhtemoc
Two options in Cuauhtemoc keep you close to the square while sitting just off the main historic-centre bustle. Hostel Mundo Joven Catedral is 290 m away, around 4 minutes on foot, and Umbral a Curio Collection by Hilton is 300 m away, about 5 minutes. Both put the Zócalo within an easy walk, which makes them handy for early mornings at the square. Order taxis through an app at night rather than hailing them, and build traffic into any plan.