Using density functional theory with a van der Waals-corrected functional, we elucidate how CO2 binds to a novel "BTT-type" metal-organic framework (MOF) featuring open metal centers. We show that CO2 binds most favorably to open metal cation sites, but with an adsorption energy that can be three times more sensitive to the choice of the bridging ligand than to metal cation choice. A strong, three-site interaction between CO2 and the open-metal site is predicted, with the binding energy enhanced by up to a factor of 2, depending on the ligand. The CO2-MOF binding can be attributed to a combination of electrostatics and vdW dispersive interactions, both of which are critically sensitive to the local environment, and both of which contribute nearly equally to the overall binding strength. We show that a judicious choice of the organic linker and the metal center allows the binding energy to be tuned from 34.8 kJ/mol (for CaBTTri) to a maximum of 64.5 kJ/mol (MgBTT).