The Roman Baths and Pump room are a must. If you can go on an evening tour. It is very atmospheric. Be wary of tasting the waters - they might do you good but they don't taste good.
Bath Abbey is very beautiful inside and out with Jacobs ladder.
Sally Lunns for a cup of tea and traditional bath bun in Abby Green. You will also find the Tourist Information Centre near here, well worth a visit.
Bath Theatre Royal if there is something on you would like to see. Very lavish inside, and do pop
into The Garrick's Head pub next do that used to be Beau Brummels House.
The Assembley Rooms and the Museum of Costumes.
Royal Crescent - No 1 is open to the public. Beautiful bath stone crescent with views across Bath.
Royal Botanical Gardens just a short walk from the crescent are well worth a visit in Royal Victoria Park which also has a large childrens play park.
Take an evening ghost walk round Bath.
Take an open top bus ride from outside the Abbey and see the sights with commentaries.
If you like more stunning architecture visit The Circus - a circle of Bath stone buildings.
Have a relaxing day in The Bath Spa - the top pool is open air with fabulous views of Bath.
The American Museum at Claverton on the outskirts of Bath.
Pultney Bridge which has shops built across the river like the traditional London Bridge. The weir and Sydney Gardens are just below.
The Avon and Kennet canal flows through the city - you can visit the row of steep locks at Widcombe which also has small villagey shops.
The Holbourne Museum whixh has a lot of craft exhibits and a new controversial glass extension. Also has a nice restaurant.
How long are you staying for? There is so much to see and do. It is Britain's only World Heritage Site. Have a great time.