The Roman Baths (BA1 1LZ) sit at the geographical centre of Bath, which means proximity to them is effectively the same as being central. Any hotel within ten minutes' walk puts you within ten minutes of Bath Abbey, the Pump Room, Pulteney Bridge, and the main shopping streets. The city is compact enough that "near the Roman Baths" and "near everything" are the same sentence.
Proximity matters most when you book timed entry slots. The Roman Baths fill quickly in summer and at weekends — the early-morning slots before 10am are noticeably quieter than the midday rush. Staying three minutes away on Beau Street, as you do at the Gainsborough Bath Spa, means you can take the first slot, return for breakfast, and go back in the afternoon if you want. From a hotel 40 minutes out of town, that flexibility disappears. The Abbey Hotel on North Parade is two minutes from the entrance on foot — close enough to drop luggage and walk straight there.
The trade-off with central Bath hotels is noise. Stall Street and Bath Street get busy on summer evenings. A room facing the street in high season means hearing the crowds until late. The Francis Hotel on Queen Square sits one street back from the busiest pedestrian routes, which makes it meaningfully quieter than options on the main drag. The Gainsborough on Beau Street is quieter still. Worth asking for a rear-facing room wherever you book — the price is the same and the sleep is better.