Liquor stores (package stores) in Texas are legally required to be closed on New Year’s Day (Jan 1) (and Sundays and certain other holidays) they cannot sell liquor that day by state law
That means none of the liquor stores listed below will be open on New Year’s Day itself for hard liquor sales. However, if you’re planning around New Year’s Eve (Dec 31) or need options like beer/wine on Jan 1, grocery stores and convenience stores can sell beer/wine and may be open (e.g., 7-Eleven, Walmart, Target).
Here’s a list of liquor stores in Dallas (for stocking up before New Year’s Day)