Like the city centre, the best way to experience northern Bath is to walk. A well trodden trail leads from the Roman Baths and Bath Abbey, up streets lined with chichi shops to the Circus and then onto the start of the Royal Crescent. Heading straight into No 1 Royal Crescent ensures you get plenty of background about the curving terrace stretching out in front of you before you stroll along its length. From there, heading back via the Royal Victoria Park, the Georgian Garden and the Jane Austen Centre is a popular approach. Although this route is arguably the most satisfying, it's also what everyone else is doing – if you're keen to dodge the worst of the crowds, do the whole itinerary in reverse.
You can manage to see all those sights in a day, before heading onto the neighbourhood's restaurants, clubs and bars. Adding another day could see you taking in the Fashion Museum, Assembly Rooms and Museum of Bath Architecture, and exploring Walcott St and taking time out in cool cafes and historic pubs.