OHenry's Coffee (https://goo.gl/maps/qVowVFsZ4EcwU2Zj7) is a cozy little coffee shop mere feet from the wedding venue. A great option if you need to sneak away for a quadruple espresso cappuccino.
Birmingham has a number of fantastic local breweries; Trim Tab (https://maps.app.goo.gl/x7z8gcDB12iNHUrHA) is one of our favorites. They have great sours and IPAs, along with cool merch and revolving art displays from local artists.
If it's cocktails you'd prefer, Mayawell (https://g.page/mayawell-bar) is a solid choice, particularly if you like tequilas.
If wine is your jam, nearby Freddy's (https://goo.gl/maps/Xu5GExnFVHA5g8YQ8) pairs a great wine list with tasty small-plate food options.