How to handle missing date data?
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).