I like Brian's answer (and I think inset maps can be really cool and informative to highlight specific portions or irregularities), but I would at first simply use a proportional symbol to represent building age (and make two maps, one with older buildings getting a bigger symbol and one with newer buildings getting a bigger symbol). The two maps are because if you have areas that are over-sampled they will likely have larger numbers of both new and old buildings.
This won't work as well if buildings are too clustered as the proportional symbols will both overlap (as you suggested in your question). Hence here is where a kernal density estimation approach (which creates a continuous heat map) could be very helpful.
I would also say summary statistics in your case can be helpful. Calculating Global measures of spatial autocorrelation (eg. Moran's I, Getis Ord, Geary's C) will be informative about the distribution. You can also map local measures of spatial association to visualize clusters of old or young buildings.