Okay, when you've had a look at the Royal Crescent, carry on up the hill, cross Julian Road and enter St James Sq. One of the houses in the bottom left corner is allegedly owned by Van Morrison housing his mistress, or rent boy, whichever you prefer to believe. Bottom right opposite the pub is a small but impressive Georgian arcade. Go up and leave by the top left corner, walk up Park Street to the top of the street (dead end). Wave at the second floor of no 21 from me for old times sake. Spot the footpath exiting the top corner of the street, walk on up and discover Lansdown Crescent, even more impressive than the Royal Crescent and definitely with better views.
See if there's live music (or lunch?) at the Bell on Walcot St. At the far end of Chatham Row, opposite the Bell, is an ice house but it's on private property and no longer accessible. The Building of Bath museum on or near Julian Road is worth a visit. The Costume museum isn't. The little park off London Road at the top end of Walcot Street is pretty and has interesting houses tucked around.
Avon Valley Cyclery next to the station, of course. And the Dark Horse on Julian Road and the St James pub should be avoided! At least they should have been 30 years ago.