Han Dold City is a city on an unspecified planet, known for being fairly dangerous. It is where warring police tribes lay ambushes for one another, where bass players get machine-gunned for playing the wrong riff too many times, and where call girls with degrees in sociology tell wealthy record company executives that it's actually okay for them to be rich.
The Old Pink Dog Bar is a far-from-harmless bar in Han Dold City where Ford Prefect discovered that Earth was not as demolished as he had previously believed. It was also here that Ford almost lost his breathing privileges after attempting to pay an extensive bar tab with an American Express card before as a last resort he offered a write-up in the Hitchhiker's Guide.
The name may be a play on 'handled' and/or 'old hand', depending on which explanations are believed.