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.