Clarence Quay I think was where the trams went, leading up to the Lord Warden Hotel. Only one pub left there now.
Have a look at this also:
http://archiseek.com/2010/1863-clarence-hotel-dover-kent/
(an Irish architectural site). The Clarence Hotel was re-named the Imperial Hotel and then the Burlington.
Originally the hotel was on the site of Clarence House the residence of Madam Sarah Rice, mother of the (later) Dover MP, Edward Royds Rice who lived at Tilmanstone.
Madam Sarah Rice was believed to be the probable 'model' on which Dickens created the character of Betsy Trotwood who shooed the donkeys off the cliffs (Madam Rice had donkeys wandering onto her lawns apparently). An interesting thought.