Can he buy permissible things from a store that sells alcohol?

Allaah has forbidden the drinking of alcohol, and He has also forbidden making it, selling it and buying it, even if it is sold  to non-Muslims. 

It was narrated from Jaabir ibn ‘Abd-Allaah (may Allaah be pleased with him) that he heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say, during the year of the Conquest when he was in Makkah: “Allaah and His Messenger have forbidden the sale of alcohol, dead meat, pork and idols.” Narrated by al-Bukhaari (1212) and Muslim (1571). 

The scholars of the Standing Committee were asked: 

Is it permissible to deal in alcohol and pork if one is not selling them to Muslims? 

They replied: 

It is not permissible to deal in that which Allaah has forbidden, whether it is food or other things, such as alcohol and pork, even if one is dealing with kaafirs, because it is proven that the Prophet (peace and blessings of Allaah be upon him) said: “When Allaah forbids a thing, He forbids its price.” And because the Prophet (peace and blessings of Allaah be upon him) cursed alcohol, the one who drinks it, the one who sells it, the one who buys it, the one who carries it, the one to whom it is carried, the one who consumes its price, the one who squeezes it and the one for whom it is squeezed. End quote. 

Fataawa al-Lajnah al-Da’imah (13/49) 

With regard to what is mentioned in the question about buying other goods from someone who sells alcohol, there is no sin in that. Allaah says (interpretation of the meaning): 

“Allaah has permitted trading”

[al-Baqarah 2:275]

The Muslims may still buy permissible things from kaafirs and evildoers, even though they also sell haraam things in other places. The Prophet (peace and blessings of Allaah be upon him) used to buy from the Jews, who consumed riba and consumed people’s wealth unlawfully. 

And Allaah knows best.