Near-field localization is expected to play a crucial role in enabling a plethora of applications under the paradigm of 6G networks. The conventional localization methods rely on complex infrastructure for providing cooperative anchor nodes that often contribute to higher network overload and energy consumption. To address this, the passive reconfigurable intelligent surfaces (RISs) can be leveraged as perfectly synced reference nodes for developing anchor-free near-field localization. First, we obtain the optimal RIS configurations that maximizes the block-wise averaged trace of Fisher information matrix so that localization error variance can be minimized across the area-of-interest (AoI). Next, we present a two-stage anchor-free localization framework wherein first a coarse estimate is obtained using cosine similarity between the coarse grid and the signal received under pre-defined optimal RIS configurations. In second stage, we refine solution similarly using a finer grid constructed around the coarse estimate. The numerical results show that the proposed RIS-aided anchor-free localization provides small root mean square error for practical values of signal-to-noise ratio (SNR), RIS dimension, and number of antennas at user.