Mai is Urdu for liquor.
Notice that is slightly different from MaiN [often written Main] which is not like English main, but Mai with a nasal sound in it. MaiN means 'I'.
So Mai in Urdu is liquor and -khaana or -khana is a suffix for a house, or store of something.
Again, notice that khaana is a complete word in itself too, which means food, or as a verb, to eat.
So Maikhana becomes a house of liquor or a store of liquor. The word can be interchangeably used for a regular alcohol shop, a bar, or a even pub. Maikhaana is a word commonly heard in Urdu ghazals.
FYI, other examples of the suffix -Khaana would be Dawaakhaana, that is a medicine shop (in old days, a doctor as well) and gareebkhana that is 'the house of the poor guy'. In Urdu, one's own house is often introduced as gareebkhaana irrespective of how rich the person may be, as a show of modesty.
Related Words: Paimaana, Saaki [Links to BollyMeaning.com]