The point of staying in Chetumal is what is around it. The Maya ruins of Kohunlich, Dzibanché and the impressive frescoes of Bonampak-style Calakmul-tier site Becán are all within a few hours by car. Closer to the city, the Laguna Bacalar — the famous "lagoon of seven colours" — is a 40-minute drive north and easily the most popular escape from Chetumal.
Across the border, Belize opens up: Corozal Town is a 20-minute taxi ride, San Pedro on Ambergris Caye an hour by water taxi from Chetumal's marina. Cheap and easy if you have the passport stamp room.