The Garrick Bar on Chichester Street is one of the better traditional pubs in the city centre, a few minutes' walk from City Hall. It's a genuine local bar rather than a tourist venue, which means the Guinness is well-kept and the prices are what you'd actually expect to pay in a Belfast pub. The bar attracts a mix of office workers, lawyers from the nearby courts, and locals who know a good pint.
The Garrick has real wooden fittings, a coal fire in winter, and no soundtrack beyond the conversation. It's the kind of bar that's increasingly rare in city centres: an entirely uncurated, unpretentious place to have a drink.