Internet-based Indoor Navigation (IIN) architectures organize signals collected by crowdsourcers in Fingerprint Maps (FMs) to improve localization given that satellite-based technologies do not operate accurately in indoor spaces where people spend 80%–90% of their time. In this article, we study the Quality-of-Position (QoP) assessment problem, which aims to assess in an offline manner the localization accuracy that can be obtained by a user that aims to localize using a FM. Particularly, our proposed ACCES framework uses a generic interpolation method using Gaussian Processes (GP), upon which a navigability score at any location is derived using the Cramer-Rao Lower Bound (CRLB). We derive adaptations of ACCES for both Magnetic and Wi-Fi data and implement a complete visual assessment environment, which has been incorporated in the Anyplace open-source IIN. Our experimental evaluation of ACCES in Anyplace suggests the high qualitative and quantitative benefits of our propositions.