No booze on the Mall. It's not BYOB either. If you want to find a bar, you have three options, head north, south, or east. Of the three, the Pennsylvania Ave strip on Capitol Hill to the east has superior options to the touristy bars just north. It's within easy walking distance of the Capitol Building. If you are over by the Lincoln Memorial, you could try your luck to the north near George Washington University.
You can also enjoy a beer at the cafe in the National Museum of the American Indian or a glass of wine or beer at the Sculpture Garden at the National Gallery.
If you are here on a summer day, bring water. The museums have plenty of water fountains, but you'll need water outside. The huge sandy park that is the Mall is fun for throwing around a football, or for letting the kids loose to chase pigeons, but all that sand and gravel reflects the awful D.C. summer humid heat. The street vendors stock water bottles in large supply, but charge a big markup—bringing a couple bottles from wherever you are staying is a good idea.