Optical tweezer arrays of neutral atoms have emerged as a promising platform for quantum science. Their geometries are highly configurable, and excitation to Rydberg states allows the atoms to interact. When driven by a laser, the system supports a rich phase diagram containing both a paramagnetic and antiferromagnetic phase. The critical point between these phases belongs to the Ising universality class, allowing our simulator to provide direct measurements of the universal scaling dimensions of the Ising conformal field theory (CFT). We adiabatically prepare the ground state at the critical point in a 1D ring of up to 40 atoms and 2D square of up to 81 atoms, and measure its spatial correlations. In 1D, we are able to extract the CFT sigma field scaling dimension of 0.127(37) by introducing a phenomenological length scale associated with decoherence. In 2D, we extract a scaling dimension of 0.59(9); however, open boundary conditions complicate the reliable extraction of a scaling dimension. In addition, the boundary phase transition supports several distinct universality classes with different critical behavior. In particular, we observe two of these classes: one where the boundary orders with the bulk and one where the boundary orders before the bulk. If time permits, progress towards a dual species optical tweezer array of Na and Cs atoms will be discussed.