If you like to walk a lot (as we do), I will mention our favorite place to stay.
https://www.lockeliving.com/en/london/locke-at-broken-wharf?
Not a traditional hotel, but an “aparthotel” with modern, compact studio apartments, plus hotel services such as a reception desk. Some rooms have views of the river, with is particularly nice at night with the bridges illuminated.
It is on the river right by the north end of the pedestrian-only Millennium Bridge, just blocks from St. Paul’s cathedral, and an easy walk to the iconic Tower Bridge and the Tower of London. Cross the bridge and you can use the riverside pedestrian path to walk as far as as you like, all with great views of the buildings lining the river.
To reach the Westminster Abbey area, we like to cross back to the north side on the pedestrian Jubilee Bridges, which line either side of the Hungerford Bridge. This puts you right in the Whitehall area of government buildings, a short walk from The Horseguards Parade, St. James Park, Westminster Abbey, Parliament buildings, and the Elizabeth Tower (aka Big Ben).
If you don’t wish to walk to, or back from, that area, you can catch the No. 15 bus right in front of St. Paul’s. It runs east-west between the Tower of London and Trafalgar Square in the heart of London, with access to Covent Garden, West End theatres, Piccadilly Circus shopping, etc. We generally use the bus to return from an evening at the theatre rather than walk back.
https://content.tfl.gov.uk/bus-route-maps/key-bus-routes-in-central-london.pdf
This location would be convenient for a daytrip that originates at Waterloo Station (Salisbury, Liverpool Street (Cambridge) or some others, but not for Bath—-you would need to transfer to Paddington for that. Or take the train to Salisbury and change there, but it takes a bit longer. Or if you book a tour to Bath (and maybe Stonehenge), it will start somewhere else, such as Victoria Coach Station for the popular Evan Evans tour.