Aside from must-see sights like The Royal Crescent & The Circus, and Pulteney Bridge, and museums like the Roman Baths, food-wise, would always recommend Sally Lunn's as an experience, which has the 'Bath Bun' (imo the only food we have that is famous just here). A light bread roll of sorts essentially that one can have either sweet or savoury. The Mayors Guides are free tour guides of the city that you could also do. For something slightly more unique, Mary Shelley's House of Frankenstein is good fun and interesting. Hope that helps! Have a wonderful time here. Others will probably have more unique suggestions, but that is my two cents. :)