How to handle missing date data? I have a column named GarageYrBlt which just lists the year the garage of that house was built.  I have one nan value for this column.  Does it make sense to fill it with the columns median (This was a common approach for the missing age values in the Titanic competition)?
I suspect you're working with the Ames house price dataset - one of Kaggle's introductory competitions.

Replacing the missing values with the dataset mean / median is very general.

I believe you have a variable which describes which neighbourhood the house is in. A more focussed approach would be to replace that missing value in GarageYrBlt with the mean / median for that neighbourhood (subject to additional sensibility checks like the garage not being built before the house).