Background: The cholinergic deficit in Alzheimer’s disease (AD) is treated symptomatically with acetylcholinesterase (AChE) inhibitors, yet current drugs suffer from limited brain penetration and adverse effects. 5,6-Dimethoxyindanone constitutes the pharmacophore of donepezil; conjugation with piperazine yields analogues with promising activity. Methods: IC₅₀ values for fifteen dimethoxyindanone–piperazine derivatives were extracted from a study employing the Ellman assay and converted to pIC₅₀ for modelling. Three-dimensional geometries were energy-minimised (MM⁺ → PM3), and 4 885 Dragon descriptors calculated. After statistical filtering (low variance, excessive missing data, inter-correlation r ≥ 0.95), 843 descriptors remained. Stepwise selection isolated four key variables—Mor22v, HATS8p, VE1_B(p) and C-006—encoding molecular volume, spatial polarizability, electronic distribution and CH₂RX fragments. An artificial neural network (MLP 4-3-1, BFGS) was trained on nine compounds, validated on three and externally tested on a further three. Results: The model reproduced experimental activity with R² = 0.961, Q² = 0.999 and MAE = 0.001 µM; external prediction yielded R²test = 0.928. Sensitivity analysis ranked C-006 as the dominant contributor, indicating that strategic CH₂RX substitution at the indanone core drives potency, while Mor22v and VE1_B(p) emphasised the favourable impact of molecular volume and electron-withdrawing groups. Conclusions: This concise ANN-QSAR model delivers accurate, mechanism-based predictions and provides tangible design rules—enhanced polarizability, optimal volume and selective halogenation—for next-generation, brain-penetrant AChE inhibitors. The workflow is fully transferable to larger libraries and multi-target optimisation, paving the way for rapid, cost-effective exploration of indanone-based chemotypes in AD drug discovery.