We can't really talk about "women" as a bloc here, because there isn't a rule that covers all women.

The early American tavern was very much perceived as a place for certain people. Enslaved and free people of color were often legally barred from entry, for instance, which made it an inherently white space. Women weren't restricted in the same way, but in general they weren't welcomed as equal patrons - respectable women would not come in for refreshment after a long day. Most public houses were meant for white men who were known to the owner as able to be trusted with credit for their meals and drinks.

The exceptions were those that ignored the regulations and standards to cater to individuals outside of this group, particularly (but not only) sailors, who were not looked on very favorably by the former type of tavern. Frequently these places were considered disorderly - partly due to the carousing, and partly due to their propensity to foment rebellion of various kinds - and local constables were often called out to deal with their noise and late-night activities. Women were more often served there, but certainly not ones that would be generally considered "respectable" by most of society, and they were as likely to be selling sex there as to be simply coming in for a drink. (Although we have to contend with the tendency of primary-source writers to frequently consider women in public spaces to be there to have sex, and to assume that women having sex outside of marriage were selling it.) By and large, women tended to consume alcohol outside of taverns.

However, yes, some public houses were owned and operated legally by women - mostly in cities, as rural areas were more likely to have limits on the number of taverns allowed, in which situations authorities preferred to advantage men. Because they would be under extra scrutiny (as individuals who were not perceived as able to command their patrons), they would usually tend to make sure that their taverns fell into the first group and that officials had no reason to consider them to be considered as running a "disorderly" house. In New York particularly, the South of the North, authorities were much more likely to prosecute women (and people of color) who broke the law against selling to enslaved people: the most important form of disorder to them. On the other hand, very marginal women - particularly poor widows and sailors' wives - were known to just acquire alcohol and put out a sign to invite customers to come and drink it in their homes, which could and frequently did result in fines for selling liquor without a license.

I would recommend Sharon V. Salinger's Taverns and Drinking in Early America (2002) for more information.