Could someone point out some relevant papers or resources (an online DB maybe?) describing the density of neurons (or, more in general, of cells) in different areas of the mouse brain?
The newest and most accurate method (far more accurate than older extrapolating/manual counting methods (Stereology) and yielding some surprising results) to estimate number/density of neurons/cells in brains is Isotropic Fractionator to my knowledge. Using this keyword you find some recent papers, comparing different brain areas (cerebral cortex, cerebellum,...) among rodents:
Combining our estimates of total cell number and percentage of NeuN-containing nuclei in each brain region, we find that adult rat cortex contains ∼80 million cells, 40% of which (∼30 million) are neurons. In comparison, rat cerebellum contains more than twice as many cells (∼170 million), >80% of which are neurons (Table 1, top). Therefore, the adult rat brain contains almost five times as many neurons in the cerebellum (∼140 million) than in the cerebral cortex. When all of the brain regions are taken into consideration, the cerebellum thus accounts for more than one-half of the cells and ∼70% of all of the neurons of the entire rat brain (Table 1, bottom). Overall, we estimate that of all of the cells in the adult rat brain, 60%, or 200.13 ± 21.17 million, are neurons. Glial cells, therefore, contrary to common belief, are not the most numerous cell type in the rat brain.
This article seems to be at least part of what you're looking for (although I can only access the abstract at the moment). They report that:
In this study the density of neurons and synapses was measured in three different areas (8, 6, and 17) of the neocortex of the mouse. [...] The total average was 9.2 × 104 neurons/mm3 and 7.2 × 108 synapses/mm3.
It would only make sense for the neuron and synapse density of the different areas of the mouse brain to be reported in the full-text article.