How to combine two time dependent datasets?
If I merge on dates, I'd have multiple repeated rows with fires occurring at the same time in different places, would that be the best way?

Probably not, since you don't want to lose the location information. You should probably find a way to map the latitude/longitude to borough/county between the two datasets, so that you obtain a semantically consistent dataset (list of fires by both date/time and location).

The problem I see is that the locations where there was no fire would not be represented, so I'd have to add a bunch of blank rows for all locations where there was no fire to balance the set.

This depends what you plan to do with your data, but given how your first dataset is currently structured (list of fires) it doesn't make a lot of sense to add locations where there was no fire. You might want to create a dataset which lists for every place and every time whether there was a fire or not, for example.