Between rstanarm and rstan, lies the vast land of brms - much more flexibility than offered by rstanarm, without the need to write Stan code yourself as with rstan. The price to pay is that you need to wait for your Stan model to be compiled - rstanarm avoids that by providing precompiled models, but that forces you to use only the included precompiled models.
To fit multilevel models with brms see
while for a generic intro see
A two-level Poisson model is pretty simple, so I reckon you shouldn't have issues fitting it with brms, but if course if it's already included in the default rstanarm models, using rstanarm will be faster.