There has been a growing interest in realizing quantum simulators for physical systems where perturbative methods are ineffective. The scalability and flexibility of circuit quantum electrodynamics (cQED) make it a promising platform for implementing various simulators, including lattice models of strongly-coupled field theories. Here, we use a multimode superconducting parametric cavity as a hardware-efficient analog quantum simulator, realizing a lattice in synthetic dimensions. Lattice sites are linked by applying pump tones at determined frequencies, realizing both hopping and pairing interactions, which can have complex amplitudes. The coupling graph, i.e., the realized model, can be programmed in situ. The realization of complex-valued interactions further allows us to simulate, for instance, gauge potentials and topological models. As a demonstration, we simulate small realizations of several paradigmatic topological models, including the bosonic Creutz ladder, the bosonic Kitaev chain, and the SSH model. We characterize the lattices with scattering measurements, reconstructing the experimental Hamiltonian and observing important precursors of topological features, including chiral transport and Aharonov-Bohm caging. This platform can be easily extended to larger lattices and different models involving other interactions. As a final example, we present a recent proof-of-principle experiment realizing a unit cell of a dynamical lattice gauge field model using three-body parametric interactions.