The Conway has a decent beer selection and serves basic bar food, though it's known for its pan-fried oysters (I am incapable of eating/judging oysters). It is said to have been established in 1932, though I do not know how soon after prohibition ended that it started as a bar. It is the lively mix of people that will likely bring you back.
Web site: conwaypub.com - facebook - KAPS youtube
Reviews: link - tripadvisor - yelp - urbanspoon