phred, thanks for mentioning the Curio Lost Property hotel. I did a search to have a look at it and I'm glad that I did. Full name:
Lost Property St Paul's London-Curio Collection by Hilton:
https://www.hilton.com/en/hotels/lonccqq-lost-property-st-pauls-london/?SEO_id=GMB-EMEA-QQ-LONCCQQ
3-5 Ludgate Hill.In sight of St Paul's Cathedral, Walk 15 minutes across the Millennium Bridge to visit Tate Modern Art Gallery, Shakespeare’s Globe theater, or Borough Market.
After looking at its location on a Google map, I'll be staying here next trip to London. Great location. And the #15 London bus comes right by the hotel and St. Paul's.
The other easy option for traveling from here is to walk down to Blackfriars Pier and catch the Uber/Thames Clipper boat to travel up or down the Thames. You can take the boat from Blackfriars Pier east to the Tower of London (Tower Pier) or onward to Greenwich. You can take the boat west to get to Westminster area for the Abbey or Churchill War Rooms.
https://www.thamesclippers.com/plan-your-journey/route-map
To the OP (Greg), full disclosure, I have not stayed at this hotel, but it sure looks good; good location; reviews are good on Trip Advisor and other sites.