Yes, Melvin, while Sunbreeze is a well respected clean hotel, it isn't known for it's "cheap"ness. Has a great pool though.
I agree the OP should try Ambergris Caye or Placencia. But until I have a better idea of what cheap means . . .i dunno what else to tell him/her.
---------- Post added July 15th, 2014 at 03:40 PM ----------
Seeing the sites in Belize can mean an extraordinary number of things and/or places. Msny places within Belize are not that easy to get to from the Cayes. Does the OP want to see ruins or is going up and down the beach to a few beach bars and restaurants going to do it for them? What is cheap? Need a budget for activities, diving and accommodations. Then myself and others should be able to be more helpful.