Immediately around Placencia there are no ruins of note, though Mayflower site is on the Southern Highway not too far away, and south of Placencia near PG (a day trip away) are Lubaantun, Nim Il Punit and other Maya sites.
In Corozal Town is the Santa Rita site, small but worth a quick visit. Across Chetumal Bay is Cerros, also small but with an interesting location on the water.
Some distance from Corozal in Orange Walk Districdt is Lamanai, along with Caracol the most interesting of Maya sites in Belize, in my opinion.
Belize First Magazine