The Public Drunkeness charge was just an excuse to pull you in. As long as you have no other charges (resisting arrest / assault), this should be pretty minor. The cost of a laywer will probably be more than the fine.

DO some research on the law in this city, and the results in similiar cases. If the cop doesn't show up, then the judge may dismiss the case. If the cop does show, your best option might be to pay a small fine and be done with it.