There is much to appreciate about Bath, and I recommend the sightseeing bus tour on day one for a complete overview of the city and its wonderful architecture.
On other days we really enjoyed the museums in Bath, dont miss a visit to number 1, The Crescent, or the Jane Austen Centre, Roman Baths of course, and there are a couple of really good art galleries too.
Follow the path alongside the Kenet and Avon canal from the Holbourne Museum through Sydney Gardens, its beautiful.
Enjoy the architecture and the river view at Pulteney Bridge, and call into the cafe opposite for a Bath Bun.
You could go horseracing at Bath Racecourse, or go to the theatre at Bath Theatre Royal, or take a day trip to Wells or Cheddar Gorge.