We have a VFW Post in town that has a bar.
I am always looking for new places to drink, but I don't know if these places are open to the public.
I am not a vet or anything. Can any old Joe walk in off the street and drink at a VFW Post?
It varies by post. In Monterey, for example, the VFW was one of the most bumpin' clubs in town, with a great house band--as long as you dig bluesy classic rock. They opened up on Fridays and Saturdays to cater to the local military, as well as students from what was then MIIS, to raise money for the post.
Others can be more restrictive, and it can be easier to get banned from them than other bars for misbehavior. Last thing you want is some jackoff provoking all the combat vets, who could and might just kill someone (i.e. most likely the jackoff, but you don't want to take chances).
If you are an attractive woman, there is almost no way you are getting turned away, no matter where you are. The smaller the town, the wider the definition of attractive, too.
I'd just ask. They may require an auxiliary membership, especially if you are in an otherwise dry county, as a way to raise money. Worst thing they can say is no.