Charge density wave (CDW) states are formed in some, typically low-dimensional, materials below a transition temperature, T_CDW. The transition of a material into a CDW state leads to the formation of a periodic charge modulation, a periodic lattice modulation, and the opening of an energy gap. While CDW states exist in many condensed matter systems, there is much to be known about the driving-mechanisms for these states as well as how these states coexist with other phases such as superconductivity. Here we present our work using scanning tunneling microscopy (STM) to study CDW states in CeTe₂, a rare-earth ditelluride with a CDW transition well over room temperature. In particular, we will present our work on quantifying nanoscale strain in CeTe₂ in an effort to better understand the local properties of the CDW states we observe.