Atomically thin two-dimensional materials, such as graphene and transition metal dichalcogenides (TMDCs), exhibit remarkable and promising optical and electrical properties for everything from solar panels to optoelectronics. These materials also offer a system to probe the effects of quantum confinement to two dimensions. For example, bound electron-hole pairs (excitons) have their Coulomb interaction modified by strict confinement to 2D. In atomically thin TMDCs, excitons can be modeled as a 2D hydrogenic system with nonlocal screening. We use reflectance contrast and photoluminescence excitation spectroscopy (PLE) to measure the energy of the excited exciton states in two TMDCs, MoS2 and WS2. Fitting the 2D hydrogenic model to our experimental results, we can extrapolate the band gap of the material and the energy required to remove the electron from the exciton (exciton binding energy). In addition to an order of magnitude increase in the exciton binding energy in 2D, 2D excitons are more sensitive to the environment around the material. We investigate the influence of changes in the dielectric environment on the exciton. We monitor how contact with a semimetallic (graphene) or insulating (BN) layer changes the energy of the excited exciton states of a 2D layer of WS2 or WSe2. The binding energy reduces by up to a factor of 2 which indicates a sensitivity promising for sensor applications.