Predicting turbulent flows under varying boundary conditions is essential in atmospheric and urban fluid mechanics, yet high-fidelity simulations remain computationally expensive. Reduced-order models (ROMs) offer an efficient alternative but typically decouple dimensionality reduction and regression into separate steps, leading to latent spaces that are not aligned with physical parameters and that are prone to error propagation. To address this limitation, we propose a condition-guided $\beta$-variational autoencoder (CG-$\beta$-VAE), which integrates a fully connected neural network (FCNN) targeted for regression into the encoder-decoder architecture. During training, the regression is performed simultaneously with dimensionality reduction, enabling the model to jointly learn latent representations and their dependence on input parameters through reconstruction, Kullback-Leibler regularization, and latent-consistency losses. The model is evaluated using two-dimensional stream-wise velocity fields from 200 large-eddy simulations of the Mock Urban Setting Test, with inflow wind direction and friction velocity as varying boundary-condition parameters. The proposed method is compared with three sequential ROMs: Proper Orthogonal Decomposition (POD)/Gaussian Process Regression (GPR), $\beta$-VAE/GPR, and $\beta$-VAE/FCNN. For unseen test conditions, the mean RMSE values are 0.32, 0.44, 0.19, and 0.14~m/s for POD/GPR, $\beta$-VAE/GPR, $\beta$-VAE/FCNN, and CG-$\beta$-VAE, respectively, while the corresponding mean $r^2$ values are 0.79, 0.44, 0.88, and 0.96. The CG-$\beta$-VAE also produces a smoother and more regression-compatible latent representation, with lower manifold cost than POD and conventional $\beta$-VAE. Qualitative comparisons further show improved reproduction of large-scale flow patterns, localized wake structures, and velocity gradients. These results show that integrating the parameter-to-latent mapping into representation learning improves both latent-space organization and predictive accuracy for parametric urban-flow ROMs.