My sister and her family live in Georgetown so we visit there several times a year but Christmas time is special (for everyone of course). The courthouse and square is lit up and decorated, there are fun events and plenty of shopping.
We stayed at the Holiday Inn Express right off of I-35, not usually my favorite location. However, we had a good experience last year and the HIE was good again this year. Separate review posted. Restaurant highlights included Uptown Social , Gumbo's and Longhorn Steakhouse. Again, separate reviews but I would recommend all of them.
If you are ever visiting the Austin area and want to see how well a town can maintain its downtown in the face of expansion, check out Georgetown. Lots of places to eat, drink and shop.